Why won't the grass grow? You'll want to take that into account when you choose what to plant in your garden. If it's poor soil or wet, containers or a raised bed could help. If it's shady, stick to greens and root crops. If it's dry, rosemary and aloe.

I would need some more info like the amount of light, orientation, and location of the space, but if you are trying to maximize the amount of plants you can grow I would definitely recommend a vertical growing tower. We build small-footprint vertical greenhouses - here is a picture of one that we built in State College, PA.