I assume that enormous amounts of energy would be needed in order to produce gravity waves.

No, even two humans dancing around each other would produce gravitational waves. However, one needs a lot of energy to produce potentially observable gravitational waves.

Could we obtain all the energy needed with the use of antimatter and some sort of thermonuclear reactor?

To produce observable gravitational waves, we need much more energy than that (orbiting black holes or neutron stars). Nothing that humans can produce.