I am interested in computing direct sum decomposition of modules over some quotients of polynomial rings over a field (do not care much about the field at this point). Does any one know a package which does that? I tried searching Macaulay 2 but could not find any. Thanks.

EDIT: Perhaps the question was a bit vague, so I will add a specific example. Let $R=k[X_{11},...X_{33}]/I$, with $k$ say, $\mathbb Q$ or $\mathbb Z/(p)$ with $p>3$ and $I$ generated by the 2x2 minors. Let $M=(x_{11},x_{12},x_{13})$. I would like to be able to understand the direct summands of syzygies of $M$. They are all maximal Cohen-Macaulay, but that's all I know.