  Recently, the theory of Topologically massive gravity non-minimally coupled
to a scalar field has been proposed which comes from Lorentz-Chern-Simons
theory \cite{1}. That theory is a torsion free one. We extend that theory by
adding an extra term which makes torsion to be non-zero. The extended theory
can be regarded as an extension of Minimal massive gravity such that it is
non-minimally coupled to a scalar field. We obtain equations of motion of
extended theory such that they are expressed in terms of usual torsion free
spin-connection. We show that BTZ spacetime is a solution of this theory when
scalar field is constant. We define quasi-local conserved charge by the concept
of generalized off-shell ADT current which both are conserved for any
asymptotically Killing vector field as well as a Killing vector field which is
admitted by spacetime everywhere. Also we find general formula for entropy of
stationary black hole solution in the context of considered theory. We apply
the obtained formulas on BTZ black hole solution, to calculate energy, angular
momentum and entropy of this soultion. We obtain the central extension term,
the central charges and the eigenvalues of the Virasoro algebra generators for
the BTZ black hole solution. We calculate energy and angular momentum of BTZ
black hole using the eigenvalues of the Virasoro algebra generators. Also we
calculate the entropy of BTZ black hole by using the Cardy formula. We find
that obtained results using two different ways are exactly matched as we
expected.
