Height doesn't seem to be linked to sex, which is surprising. I have seen ways to predict children's height and it involves taking the average of both parents height. Upon my search, I did not find the actual gene for height.
No single gene determines the height (a polygenic trait) of an individual. In fact, height is coded for by over 700 genes. Also, I'm caught quite off guard by your suggestion that height isn't linked to sex, which is obviously not true. One gene that is associated with a shorter height (to put it simply), ITM2A, is expressed more strongly in women and so helps explain a small (though not inconsequential) fraction of the height difference between men and women.