Anything metal, that is outside your home, and connected to something inside your home should be properly "grounded", regardless of its height/location... but I don't know of any code forcing you to do so. The only "grounding" codes I'm aware of are those pertaining to the electrical service panel.
But be aware, if “grounding” is done improperly it has the potential to do more damage than no “grounding”. Grounding to conduit, duct work, plumbing and whatnot is not correct, it is not the same as connecting to the service panel ground... it has the potential to create separate ground paths or planes and can be extremely dangerous (more about that in a minute).
And funny thing about lightning and grounding protection… it don’t always follow the “rules”.
For example, once we had lightning strike a metal grain leg on top of a concrete silo at a large farm cooperative. We had four point-to-point data radios/antennas mounted on the outer walls of the concrete head house. When first installed, all four were grounded to the metal electrical conduit (which, in this case is OK because its an outdoor concrete structure and the conduit was outside, putting the radios on the same ground plane as the electrical service ground). At some point one of the radios failed and had been replaced; the guy who did the replacement forgot to hook up the ground (might have been me?). Anyway, of the four, only the non-grounded radio survived… the other three were completely destroyed.
We have radio equipment installed on hundreds of different towers, grain legs, and other structures spread-out over five states… some of them several hundred feet in the air. Most of those structures have never been struck by lightning (at least, not hard enough to damage the equipment)... yet there are a few that get hit once or twice every single year without fail. And I don’t mean just a little hit… they get hit hard enough to totally wipe-out all the radio equipment, take out all the electrical service and even get to any sensitive electronics in surrounding buildings. Heck, one grain leg just thirty miles from here got hit six friggin’ times in just one spring/summer season!!! We built a tower for farm cooperative in Illinois a few years ago, just two years later they had us come take it down… because lightening had struck it eight times in those two years, wiping-out all the office computers every time!!! So much for the old saying, “Lightening never strikes in the same place twice.”
Living out in the sticks I was forced to use a dial-up internet connection for years and lost three computers in that time from lightening strikes (well, assuming lightening). All three times it came in on the phone line, taking out the computer, phones, and anything else connected to the phone line (like the satellite TV tuner)… once it even blew some of the modular connector boxes clean off the walls!! But I’ve never once had my TV antenna tower get touched… it’s likely the tallest thing for a mile radius at least, the damn phone line is underground!!
OK, the proper way to ground a vertical steel structure, such as a metal chimney entering your home. You need two [copper ground wires, 6 gauge minimum… one should be connected above the roof near the top, the other should be connect inside the home close to the stove. Both wires need to be connected to the electrical service panel earth grounding wire… either inside by the panel, or outside where it enters the earth. This puts everything in the home on the same ground plane… two separate ground planes can actually cause the “zap” to travel all through the house as it heads for the “other” ground, or even go out on one and back in on the other. In the case of a “strike” the top ground wire should route most of the “zap”, the bottom wire routes any left-over or transient charge. But a more common cause of (so called) “lightening strike” damage isn't caused by an actual “strike”, and this is where the two ground wires are most important. During storms the wind and rain cause friction in the air and on the structure causing a static charge build-up… and as well, lightening in the vicinity can add to this “build-up”. At some point this charge can become large enough that it starts looking for somewhere to go. If it goes down the spout the lower wire will route it away from you and your “stuff”, if it heads up the spout you need a wire there to route it to earth or it can actually attract a full-fledged massive direct-hit lightening “strike” (like the ones that turn trees into tooth picks)… and in the case of a full-fledged “direct-hit” there ain’t enough grounding wire on the planet that can protect you and your "stuff".