  In this paper, we investigate surfaces in singular semi-Euclidean space
$\mathbb{R}^{0,2,1}$ endowed with a degenerate metric. We define $d$-minimal
surfaces, and give a representation formula of Weierstrass type. Moreover, we
prove that $d$-minimal surfaces in $\mathbb{R}^{0,2,1}$ and spacelike flat zero
mean curvature (ZMC) surfaces in four-dimensional Minkowski space
$\mathbb{R}^{4}_{1}$ are in one-to-one correspondence.
