Hi
Do a google on the word "Aquaponics" there is tons of info on the internet.
I've dabbled a bit in the method but mostly for ornamental fish. Have nevr tried it for food. Good luck gary

IMO it's just a gimmick to make the builder rich. You can't grow large enough fish to eat in it and it won't produce enough or a balanced fertilizer for healthy plants. Don't fall for their BS!

CC
I am just starting out in this method of growing fish (Blue gill) and veggies. the fish and the veg are doing quite well. The system that I modeled uses the 275 gal water tanks and some plastic trays that were from a motor-home (storage trays)I used expanded clay ( Hydroton) in some of the beds and pea gravel in the others, the next set of beds I'll use expanded shale as the grow medium. The easiest method for the beds is to use the fill and dump system, basically foolproof. There is some great info and a forum at www.aquaponics.net.au Also some videos on you-tube for aquaponics.

Your dimensions sound ok but you did not give a depth.
It will probably be a challenge at first in getting plants to grow. Be sure to research out what plants are best for this use. Also on the fish use only plant feeding fish, not game fish as game fish will not survive unless they have feeder fish to live off of, the feeders would be plant eating fish.
I have done something like this by accident but not using plants to feed off of. What I discovered is that catfish will grow remarkedly large in small pools provided they have abundant plant matter to feed off of. And the pool does not have to be very deep either.
Tilpia is what seems to be the preferred fish.
Do your research and take your time in working out your system. It won't happen overnight. Probably take a couple of years to really get the hang of it.

I would start out with a system much smaller than what you have mentioned. I set up a very small setup in my apartment a couple years ago with mixed success. I learned enough from that 30 Gallon setup to be more confident with a larger system. On the other hand, I saw horticulture professors at a local college consistently kill fish from inexperience in there large setup. Perhaps start with part of your designated space and build it up over time. Here are some articles I found particularly helpful:

https://attra.ncat.org/attra-pub/PDF/aquaponic.pdf

http://www.backyardaquaponics.com/Travis/Aquaponics_Common_Sense_Guide.pdf

There have been a few iterations of this one, but his early one was one of my favorite resources for my setup.
http://www.aces.edu/dept/fisheries/education/documents/barrel-ponics.pdf