Does there exist a Gorenstein local ring $R$ such that $R/\sqrt 0$ is not Cohen-Macaulay?

Question

Does there exist a Gorenstein local ring $R$ such that $R/\sqrt 0$ is not Cohen-Macaulay?

Note that since $1$-dimensional reduced rings are Cohen-Macaulay, so for such an example, we must have $\dim R\ge 2$.

Thanks in advance.