  We prove an invariant Harnack's inequality for operators in non-divergence
form structured on Heisenberg vector fields when the coefficient matrix is
uniformly positive definite, continuous, and symplectic. The method consists in
constructing appropriate barriers to obtain pointwise-to-measure estimates for
supersolutions in small balls, and then invoking the axiomatic approach from
[DGL08] to obtain Harnack's inequality.
