The classical Weierstrass transform is an isometric operator mapping elements of the weighted $L_2-$space $\mathcal{L}_2(\mathbb{R}, \exp(-x^2/2))$ to the Fock space. It has numerous applications in physics and applied mathematics. We defined an analogue version of this transform discrete Hermitian Clifford analysis, where functions are defined on a grid rather than the continuous space, in dimension $1$. This transform is based on the classical definition, in combination with a discrete version of the Gaussian function and discrete counterparts of the classical Hermite polynomials. The aim of this talk is to extend the definition for $1$ to higher dimensions, where we must take into account the anticommutativity of the basic Clifford elements and use the generalised discrete Hermite polynomials. Furthermore, we investigate, again in dimension $1$, what happens if the mesh width approaches $0$.