  In this paper we investigate Leibniz algebras whose quotient Lie algebra is a
naturally graded filiform Lie algebra $n_{n,1}.$ We introduce a Fock module for
the algebra $n_{n,1}$ and provide classification of Leibniz algebras $L$ whose
corresponding Lie algebra $L/I$ is the algebra $n_{n,1}$ with condition that
the ideal $I$ is a Fock $n_{n,1}$-module, where $I$ is the ideal generated by
squares of elements from $L$.
