Modularity Density Maximization is an optimization problem with the objective of solving non-overlapping instances of the clustering problem know as Community Detection in networks without having the resolution limit of the Modularity Maximization method. In the literature, it is not know of any linear programming model that can give the exact solution for instances with more than 40 vertices. This limitation occurs because of the high number of variables needed to solve the problem. There is a mathematical optimization method know as Column Generation that can be applied to linear optimization problems to reduce the number of variables needed to solve it. Thus, the objective of this work is to apply the Column Generation heuristic to the Modularity Density optimization problem to solve instances with more than 40 vertices.