  Let $L$ be a line bundle over $M$. In this paper we associate an
$L_\infty$-algebra to any $L$-Courant algebroid (contact Courant algebroid in
the sense of Grabowski). This construction is similar to the work of Roytenberg
and Weinstein for Courant algebroids. Next we associate a $p$-term
$L_\infty$-algebra to any isotropic involutive subbundle of $(\mathbb{D}L)^p :=
DL \oplus (\wedge^p (DL)^* \otimes L)$, where $DL$ is the gauge algebroid of
$L$. In a particular case, we relate these $L_\infty$-algebras by a suitable
morphism.
