No the human cannot hold the copyright also. They can own the property rights to the code and protect it. It's not like the rule is "AI cannot copyright stuff but humans can" but rather code is rarely copyrighted and in its case, ownership is much more important.

If your code was generated by you and you store it in your system and have property rights over it, you can enforce legal actions even without holding a copyright over the code.

In general, it is kind of weird to want to copyright code. How do you patent a for-loop for example