  Let $\mathfrak{o}_2$ be a finite principal ideal local ring of length 2. For
a representation $\pi$ of $GL_{4}(\mathfrak{o}_2)$, the degenerate Whittaker
space $\pi_{N, \psi}$ is a representation of $GL_2(\mathfrak{o}_2)$. We
describe $\pi_{N, \psi}$ explicitly for an irreducible strongly cuspidal
representation $\pi$ of $GL_4(\mathfrak{o}_2)$. This description verifies a
special case of a conjecture of Prasad. We also prove that $\pi_{N, \psi}$ is a
multiplicity free representation.
