Observations of T-Tauri circumstellar discs show the presence of mm or cm size dust grains at large distances from the central star (r > 10s AU). There empirical data challenge the currently mainstream grain growth theory, that disfavours the formation of such large grains in the outer disc and, despite formation, predicts their rapid inward migration due to coupling with the gas on short timescales. In this work, we develop some improvements in the grain growth theory and implement them in GrOG (Growth Of Grains), a new numerical solver for the coagulation and fragmentation of grains inside a circumstellar disc. Our results revise conclusions from previous theoretical models, as we are able to growth particles of significantly larger size.