  We discuss a natural extension of the AKSZ construction to the case where the
source is given by a supermanifold with a chosen integral form. We then focus
on the special case with the target given by a Courant algebroid. In the
simplest case this leads to the BV version of the super Chern-Simons theory, as
developed by Grassi-Maccaferri and Cremonini-Grassi. In the case of exact
Courant algebroids we derive the 2-dimensional $\mathcal N=(1,1)$ sigma model
on the boundary, together with the Wess-Zumino term, paralleling the approach
of \v{S}evera in the bosonic case.
