$M$ finitely generated over $(R,\mathfrak{m})\Rightarrow M/\mathfrak{m}M$ artinian

Question

Let $(R,\mathfrak{m},k)$ be a commutative noetherian local ring and let $M$ be a finitely generated module over $R$.

Is $M/\mathfrak{m}M$ artinian? Since $M/\mathfrak{m}M$ is noetherian it is enough to show that it has finite length but I am not able to see it. Can someone help (if it's true)?