Non-minimal Krull associated primes of a PF-ring

A commutative ring $$R$$ is said to be a PF-ring if every principal ideal of $$R$$ is a flat $$R$$-module. Also, a prime ideal $$P$$ of $$R$$ to be a Krull associated prime of $$R$$ if for every element $$x\in P$$ , there exists $$y\in R$$ such that $$x \in ann_R(y)\subseteq P$$, where $$ann_R(y):=\{r\in R\mid ry=0_R\}$$.

I am looking for a PF-ring with a Krull associated prime ideal $$P$$ such that $$P$$ is not a minimal prime ideal of $$R$$, that is, there exists a prime ideal $$Q$$ of $$R$$ with $$Q\subseteq P$$ and $$Q\not= P$$.