The large gray box on the bottom left is the Antimatter Fuel Container, which feeds into the bottom end of the Vertical Intermix Chamber
I personally don't think that the Antimatter Fuel Container would be that large (Assuming it's the big grey thing, if it's the circular thing, different story)
1 gram of antimatter is about 3 hiroshima bombs worth of explosive energy.
Another thing to point out is that antimatter must be kept from touching any matter, this would mean keeping it in a vacuum, magnetically kept away from the walls. If it were to touch a wall of it's container, the resulting explosion would be horrific.
I don't know what the star trek version of antimatter would do, but this is real life antimatter I'm talking about.
I figure it is the Antimatter storage, including all self-contained magnetic bottles, "plumbing" and ejector mechanisms. I don't really see it as simply a large box of antimatter. It only makes sense that the Antimatter storage be a very self-contained, self supporting, self-ejecting system. What is the real volume of Antimatter in that containment system? I don't know. Please remember, that much of this is a rough-in, large empty spaces that really aren't empty, large solid blocks that really aren't solid, etc.
If I still have the will/time/energy once the basic build is done, I'll go back and add some of those details where appropriate.