I agree, Codiaeum (commonly called Croton) and it reminds me of
Banana Croton (Codiaeum variegatum 'Banana')
From what I can see, the soil looks extremely dry and the leaves look as though they are covered with thick dust and/or dirt. I'd take wet paper towels and wash off the leaves, water the plant thoroughly, until water drains out the bottom of the pot (discard any water remaining in the saucer or outer pot) and give it as much bright light as possible. Once your weather warms up, you might try to find a spot outside where it can receive fresh air and bright light.
