Let $R$ be a Noetherian commutative ring. If $R$ is local, then $R$ is Gorenstein if $inj.dim(R)<\infty$. Otherwise $R$ is Gorenstein if $R_P$ Gorenstein for all prime ideals $P$.\
There is a simple result stating that $inj.dim(R)<\infty$ if and only if $R$ is Gorenstein and it has finite Krull dimension, and I proved it. My question is, is there any ring that is Gorenstein and has infinite Krull dimension?