Nilpotent Lie Algebra with determinant 0

Question

If I have a nilpotent Lie Algebra $\mathfrak{g}$ and a representation $\rho(X)$ in a vector space $V$ such that $det \rho(X) = 0 $ for all $X \in \mathfrak{g}$, then how do I show that there is a vector $v \in V$ such that $\rho(X)v = 0$ for all $X \in \mathfrak{g}$? I know it involves Engel's theorem but I'm not sure how.