Is any Finitely generated module over an Artinian ring , Noetherian?

Question

In order to prove a statement, I need to prove the following claim :

If $R $ is an (not necessarily commutative) Artinian ring and $M $ is a finitely generated $R $-module, then $M$ is Noetherian.

I know that If $R $ is an Artinian ring and $M $ is a finitely generated $R $-module, then $M$ is Artinian.

What about the claim?Is there any hint to prove that? Or any counterexample?

Thank you