Let $S=k[x_1,...,x_n]$ be a polynomial ring over field $k$ with maximal ideal $m=(x_1,...,x_n)$. I wanna make a $3$-dimensional $S$-module $M$ such that $H^0_m(M)=H^1_m(M)=0$ and $H^2_m(M)\neq 0$ be finitely generated (or in general case: $H^i_m(M)$ be finite for all $i=0,1,2$ ). Is there a simple way to create similar examples(for any dimension)?

**Background:**

$H^i_m(M)$ means $i$'th local cohomology module of $M$.