I second Trefarmer's lighting calculations- 2000 watts is drastically insufficient for 12x12, and even 4000 watts is marginal. The standard calculation for 1000 watts is 4x4, or 16 square feet. 12x12=144 square feet. 144/16= 9 lights to get similar lumens per square foot. Yes, it's true you'll need to actively cool such a room, but that's hardly unusual. Look around the Farm, you'll quickly see some of the most productive gardens adhere to these rules.
There are some cheats, and I'm working on one. But if oyu want yields, you need light. And it doesn't matter how many plants you have, if they're big enough to cover the area they're going to give you yield.