  This article constructs a smooth weak Fano threefold of Picard number two
with small anti-canonical morphism that arises as a blowup of a smooth curve of
genus 5 and degree 8 in $\mathbb{P}^3$. While the existence of this weak Fano
was known as a numerical possibility in \cite{CM13} and constructed in BL12,
this paper removes the dependencies on the results in \cite{JPR11} needed in
the construction of BL12 and constructs the link in the style of ACM17.
