Example of module on dimension $d$ with trivial local cohomology $H^d_I(M)$.

Question

Let $R$ be a Noetherian ring, $I$ is an ideal. Are there examples of an $R$-module $M$ such that local cohomology $H^d_I(M)=0$, where $d=\dim M$.

It is well-known that there are no such examples over local Noetherian rings. It is also not hard to show that $H^i_I(M)=0$ for $i>d$ for any Noetherian ring.