AutoCAD, Zemax Optic Studio 15, and Interactive Data Language (IDL) with the Proper Library are used to computationally model and test a diffractive mask (DiM) suitable for use in the Gemini Multi-Conjugate Adaptive Optics System (GeMS) on the Gemini South Telescope. Systematic errors in telescope imagery are produced when the light travels through the adaptive optics system of the telescope. DiM is a transparent, flat optic with a pattern of miniscule dots lithographically applied to it. It is added ahead of the adaptive optics system in the telescope in order to produce diffraction spots that will encode systematic errors in the optics after it. Once these errors are encoded, they can be corrected for. DiM will allow for more accurate measurements in astrometry and thus improve exoplanet detection. The mechanics and physical attributes of the DiM are modeled in AutoCAD. Zemax models the ray propagation of point sources of light through the telescope. IDL and Proper simulate the wavefront and image results of the telescope. Aberrations are added to the Zemax and IDL models to test how the diffraction spots from the DiM change in the final images. Based on the Zemax and IDL results, the diffraction spots are able to encode the systematic aberrations.