  We answer in the affirmative a question posed by Ivanov and Vassilev on the
existence of a seven dimensional quaternionic contact manifold with closed
fundamental 4-form and non-vanishing torsion endomorphism. Moreover, we show an
approach to the classification of seven dimensional solvable Lie groups having
an integrable left invariant quaternionic contact structure. In particular, we
prove that the unique seven dimensional nilpotent Lie group admitting such a
structure is the quaternionic Heisenberg group.
