I've been living in Hokkaido for a while now, and there are plenty of dinky buildings on flat surfaces that have ハイツ stuck on the end of their names. As a native English speaker, few of these are places I would call "Heights".
I did a bit of googling and 知恵袋 states beyond the English definition that it shows up in building names.
What does it mean in Japanese to call a building ~~ハイツ?