Non-perfect ideal $I$ such that $\mathrm{projdim}(R/I)<\infty$

Question

Let $R$ be a Noetherian local ring. A proper ideal of $R$, $I$ is called perfect if grade$(R/I)=$projdim$(R/I)$ where grade$(R/I)=$depth$_IR$ and projdim$(R/I)$ is the projective dimension of $R/I$.

Is there an example of a non-perfect ideal $I$ with projdim$(R/I)<\infty$?

Fact : Since $I$ is not perfect, projdim$(R/I)>$grade$(R/I)$.