We present the results of the HIGHz Arecibo survey, which measured the HI content of 39 galaxies at redshift $z>0.16$ selected from the Sloan Digital Sky Survey. These are all actively star-forming, disk-dominated systems in relatively isolated environments, with stellar and HI masses larger than $10^{10}$ M$_odot$ and redshifts $0.17leq zleq 0.25$. Our sample includes not only the highest-redshift detections of HI emission from individual galaxies to date, but also some of the most HI-massive systems known. Despite being exceptionally large, the HI reservoirs of these galaxies are consistent with what is expected from their ultraviolet and optical properties. This, and the fact that the galaxies lie on the baryonic Tully-Fisher relation, suggests that HIGHz systems are rare, scaled-