This question is a follow up of the following answer I posted recently:

Is there a second order partial differential operator with **real** coefficients which are not solvable in Lewy sense? I am also not aware of first and third order operators but I thought second order operator is a natural question as we may be able to apply some conjugations of known first order non-solvable Lewy like operators with complex coefficients. In this direction, Mizohata's example $\frac{\partial }{\partial x}+ix\\frac{\partial }{\partial y}$ was not helpful as it is giving me Grushin like operators whose solvability is proved.