Your sentence is fine, Ilham. Home in your example is behaving like an adverb expressing direction. We do not need a preposition with home when it is used with any verb referring to direction: ...

It's a preposition that can indicate duration, direction or distance. For example: I drove from Los Angeles to San Francisco. We're open from Monday to Friday. She walked three to four blocks out ...

So, because there’s no movement, the dative case dem Tisch has to be used after the dual case preposition unter. Of course, it’s not just unter that behaves like this. Here’s an example of ...