We consider congruences of multisecant lines to a non
linearly or non quadratically normal variety of codimension two or three
in a projective space. We give a uniform way to compute the degree of
the dual variety of their focal locus. Then we focus on the geometry
of the non quadratically normal variety of codimension three in Pg. In
particular we construct a component of the double locus of its dual from
the Hyper-Kahler 4-fold of Debarre-Voisin.