  We consider second order linear degenerate-elliptic operators which are
elliptic with respect to horizontal directions generating a stratified algebra
of H-type. Extending a result by Guti\'errez and Tournier for the Heisenberg
group, we prove a critical density estimate by assuming a condition of
Cordes-Landis type. We then deduce an invariant Harnack inequality for the
non-negative solutions from a result by Di Fazio, Guti\'errez, and Lanconelli.
