Examples of an indecomposable finitely generated module over a local ring.

Question

Let $R$ be a local ring, that is, there is only one $\mathfrak{m}$ maximal ideal. It can be proved that for a module $M_{R}$ over $R$ which is finitely generated, $M_{R}$ has always a projective cover and if so this projective is given by $\rho:R^{(n)} \to M_{R}$ where $n$ is the dimension of $R/\mathfrak{m}$-module $M/\mathfrak{m}M\cong (R/\mathfrak{m})^{n}$. I want to show an example of an indecomposable finitely generated module over $R$ local so I need $n>1$. I was thinking over vector spaces but this is not gonna work since all indecomposable vector spaces have dimension $1$. Any help showing an example satisfying this will be appreciated. Thanks