So, for a projective variety $X$ over, say, an algebraically closed field $\Bbbk$, being normal implies being regular in codimension one. However, the converse is not true, in addition you require an extension property. I am looking for an example of an $X$ which is regular in codimension one, but not normal.
By common lore, this can not be a curve or a surface in $\Bbb P^3$. I was hoping that maybe there is an example of a surface in $\Bbb P^4$. Beating around the bush less: I would like a small and explicit example if possible.
