Simply cooking carbon or anyother element in a nuclear reactor is not going to provide ß+ decaying radio isotopes. You probably want to look at the fission products (and their daughters) in spent fuel rods. This may be an awfully expensive way to get anti-electrons. I'm not sure it's cheaper than running a linear accelerator. I'm pretty sure it's more expensive than the usable energy you get out of the two .511 MeV gamma ray. It's hard to extract electricity from neutral particles.

I guess I don't understand why you were fixating on C11. If you look at the Chart of the Nulcides you'll see a curve of stable isotopes. Above that curve you'll find many isotopes that have a ß+ decay mode. Below it you'll find many isotopes with a ß- decay mode.

Dave M