The minimum recommended size habitat for a single small – medium sized rabbit is 4′ X 2′. In NIC terms that’s 3X2 grids and at least 2 grids high. 

Here’s a visual of that:

I’m not sure I understand your height limitations? If you only have room for less than a grid tall then I do not think that would be tall enough. They need to have enough height to fully stand up on their hind legs. 

Do you have any other space that would work for a bunny habitat? 

Edited to add: A single grid is 14″ X 14″.