Principal Radical Ideal

Question

Let $R=k[x_0,\ldots,x_n]$ be a standard graded polynomial algebra over a field $k$ ($k$ can be algebraically closed if you want). Is there a homogeneous prime ideal $P\subset R$ for which the integral domain $R/P$ has no non-trivial principal radical ideal? I am asking because I recently stumbled across Proposition 15.111.10 on the Stacks Project, which makes me believe that such creatures might exist, but I'm having trouble coming up with $P$'s that aren't Cohen-Macaulay or normal...if someone knows an example or a reference that would be great :-)