New building code does not apply to older construction. So your statement "is my old house violating the new code" has no meaning. When injury occurs, your liability will be reviewed by the fact itself. The code would not apply in the determination of your liability.
Which means, your injured tenant cannot use the new code to prove your negligence, but he can use other evidence in the injury case. In any case your insurance company is likely to cover your liability because your building complies to the code at the time of the construction.
This is not a legal advice because I have not studied your state and local law. Just common sense.