The research of stars with the B[e] phenomenon is still in its infancy, with several unanswered questions. Physically realistic models that treat the formation and evolution of their complex circumstellar environments are rare. The code HDUST (developed by A. C. Carciofi and J. Bjorkman) is one of the few existing codes that provides a self-consistent treatment of the radiative transfer in a gaseous and dusty circumstellar environment seen around B[e] supergiant stars. In this work we used the HDUST code to study the circumstellar medium of the binary system GG Car, where the primary component is probably an evolved B[e] supergiant. This system also presents a disk (probably circumbinary), which is responsible for the molecular and dusty signatures seen in GG Car spectra. We obtained VLTI/MIDI data on GG~Car at eight baselines, which allowed to spatially resolve the gaseous and dusty circumstellar environment. From the interferometric visibilities and SED modeling with HDUST, we confirm the presence of a compact ring, where the hot dust lies. We also show that large grains can reproduce the lack of structure in the SED and visibilities across the silicate band. We conclude the dust condensation site is much closer to the star than previously thought. This result provides stringent constraints on future theories of grain formation and growth around hot stars.