We investigate the properties of a model of granular matter consisting of N Brownian particles on a line, subject to inelastic mutual collisions. This model displays a genuine thermodynamic limit for the mean values of the energy, and the energy dissipation. When the typical relaxation time tau associated with the Brownian process is small compared with the mean collision time tau(c) the spatial density is nearly homogeneous and the velocity probability distribution is Gaussian. In the opposite limit tau much greater than tau(c) one has strong spatial clustering, with a fractal distribution of particles, and the velocity probability distribution strongly deviates from the Gaussian one