  In this paper we construct a map between a solution of supersymmetric
Chern-Simons higher spin gravity based on the superalgebra $sl(3|2)$ with
Lifshitz scaling and the $N=2$ super Boussinesq hierarchy. We show that under
this map the time evolution equations of both theories coincide. In addition,
we identify the Poisson structure of the Chern-Simons theory induced by gauge
transformation with the second Hamiltonian structure of the super Boussinesq
hierarchy.
