My understanding (belief) is that it's going to depend on how much human involvement is there.

If you write a prompt and one-shot a problem and share the source code, that source code is probably not covered by copyright.

If you substantially edit or modify the generated code you would own the copyright.

It's like with a camera. If I set a camera and carefully aim it and somehow trigger the shutter then make adjustments in Photoshop, I own the copyright on that image.

If I stick a Flock camera on a pole somewhere and post the live output, there's been no meaningful human creative involvement in producing those images and so nobody can claim copyright on them.