  In this work, we examine a family of $pp$-wave solutions of Minimal Massive
3d Gravity (MMG) minimally coupled with the Maxwell-Chern-Simons theory. An
elaborate investigation of the field equations shows that the theory admits
$pp$-wave solutions provided that there exist an anti-self duality relation
between the electric and the magnetic components of the Maxwell 2-form field.
By employing Noether-Wald formalism, we also construct Noether charges of the
theory within exterior algebra formalism.
