your headline asks how to appeal a building code violation--the jurisdiction enforcing the code likely has an appeal process--likely online, that you can review.
Owners can be held responsible for damage inside the leased property (burst pipes, leaky gas connections, walls, jammed and swelled window frames, pest infestations, bathroom floors/tiles that come loose ceilings, floors that give way, or any of dozens of other issues associated with a building aging and even normal wear and tear.
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If you wish to appeal a local ordinance violation, you need to contact the municipality and learn about their process. Although the owner may be ultimately liable for whatever violation the village has found, the owner can assess those damages against the tenant.