We use code D5865 for a complete mandibular overdenture, but it only pays about $1000. Our cost is about $4000. Is there a different code we are supposed to use or is there an additional code that I should use?

The ADA gives instructions on coding for overdenture. It's not only the overdenture but also each precision attachment that you would code for. Hope that helps!
https://www.ada.org/-/media/project/ada-organization/ada/ada-org/files/publications/cdt/cdt_overdenturecodingguidance_naturaltoothborneandimplantborneprostheses_2020nov.pdf

Without knowing the specifics, yes, D5863 is the correct code for overdenture- complete mandibular regardless of reimbursement. Now if you are performing other procedures during this time those may be coded out along with the prosthetic service. It is important to review the documentation and code for all services provided.