How can I support a large aquarium built into a wall?
Static load affects structures much differently than dynamic (moving) load. A dynamic load will give periods of relaxation for members to return to their previous shape. A static load will promote bending. Considering the pressure and surface area, you basically need this to sit on your slab.  The tank can't take pressure, and you don't want the tank pulling your house down via the wall it is attached to, so for the house, you're basically building a 12 foot wide door, and a tank that's just under the door frame. 

The rest is planning for eventual water spill and easy maintenance. 

Most aquarium frames capable of holding a 2 foot by 2 foot cross section aquarium are made from 2x4 with 3/4 inch plywood facing.  They use a ladder frame for the top and bottom, and have vertical members spaced every 2 feet.  The exceptions to these rules include removing every other run in the floor frame (to accommodate sump equipment) and ever other riser on the access side of the frame (to accommodate repairing / replacing the sump equipment).  Reinforce the frame as you see fit (most are very overbuilt), as skimping on a little extra 2x4 can buy you a lot of sleepless nights.  

Build a pan into the frame if you can.  Build a drain into the room if you can.  Keep in mind that you'll need storage space for water treatment, and access to the top of the tank.  The best solution is a "aquarium closet" with an extra tank just under 1/2 the size of your aquarium.  If possible, build that room like a shower, with a central drain, and greenboard around the floor area.  In the event that your aquarium develops a leak, it will probably do so when you're on vacation :) 

Pay attention that the frame is level and solid on the floor.  After you fill the aquarium it will not rock, but those warnings about static load apply to the frame too.  If the frame bends, the glass sheets will encounter stress along the seams, and you will get a leaky seal between the sheets.

Ironically, at your size you really shouldn't be messing with anything except a reef-ready tank, which conveniently comes with holes drilled in the bottom :) (for those who don't know, that's a good thing as sump equipment is stored below the aquarium)