We present our ongoing work on two-dimensional maximally supersymmetric Yang--Mills (2D MSYM) theory using lattice techniques. The continuum theory is obtained from the dimensional reduction of four-dimensional ${\mathcal N} = 4$ supersymmetric Yang--Mills theory. We construct both the continuum and lattice versions of the 2D MSYM theory. The lattice action preserves a subset of supersymmetries. We extend existing lattice software with new routines to accommodate the additional terms in the lower-dimensional theory. This lattice construction enables us to perform Rational Hybrid Monte Carlo simulations of 2D MSYM and facilitates the exploration of its continuum limit. Our work contributes to the numerical study of maximally supersymmetric gauge theories and supports the ongoing efforts to test gauge--gravity duality and investigate related non-perturbative phenomena.