  We show that the strata $ \mathcal{M}_{11,6}(k) \subset \mathcal{M}_{11} $ of
$ 6-$gonal curves of genus $ 11 $, equipped with $k$ mutually independent and
type I pencils of degree six, have a unirational irreducible component for
$5\leq k\leq 9$. The unirational families arise from degree $ 9 $ plane curves
with $ 4 $ ordinary triple and $ 5 $ ordinary double points that dominate an
irreducible component of expected dimension. We will further show that the
family of degree $ 8 $ plane curves with $ 10 $ ordinary double points covers
an irreducible component of excess dimension in $ \mathcal{M}_{11,6}(10) $.
