  We provide the first examples of strongly dense representations of a
hyperbolic 3-manifold group into $SL(4,\mathbb{R})$ and $SU(3,1)$ i.e.
representations where every pair of non-commuting elements has Zariski dense
image. Our examples are holonomy representations arising from projective
deformations of its hyperbolic structure. As a Corollary, we get that
$SL(4,\mathbb{R})$ has non-Hitchin strongly dense surface subgroups.
