  We prove that the moduli space of Calabi-Yau 3-folds coming from eight planes
of $P^3$ in general positions is not modular. In fact we show the stronger
statement that the Zariski closure of the monodromy group is actually the whole
$Sp(20,R)$. We construct an interesting submoduli, which we call
\emph{hyperelliptic locus}, over which the weight 3 $Q$-Hodge structure is the
third wedge product of the weight 1 $Q$-Hodge structure on the corresponding
hyperelliptic curve. The non-extendibility of the hyperelliptic locus inside
the moduli space of a genuine Shimura subvariety is proved.
