Growing enough grain to feed yourself takes 400 - 1000 m² depending on soil fertility.
So you can't do that in your backyard. It's also dramatically more efficient to harvest grains with big machinery, so it's wise to put it together with your neighbours and form something like a cooperative.
That's like a 32m x 32m field, not as big as I was expecting. But yes, larger fields are more efficient. I wonder if there is some reasonable setup for farming grains with aquaponics. (Rice doesn't count XD)
Also beware, that grains need direct solar irradiation (they need to collect lots of energy, much more than vegetables), so stacking them on top of each other is not viable.