  In this paper, we consider generic corank 2 sub-Riemannian structures, and we
show that the Spherical Hausdorf measure is always a C^1-smooth volume, which
is in fact generically C^2- smooth out of a stratified subset of codimension 7.
In particular, for rank 4, it is generically C^2 . This is the continuation of
a previous work by the auhors.
