In nature, Coulombic fluids are present in many different forms, for instance, as aqueous electrolytes dissolving charged biomolecules (such as the DNA or lipid bilayers), macroion or nanoparticle solutions, molten salts, ionic liquids, plasmas, etc. One important characteristic of charged fluids is the long-range electrostatic interaction, which must be incorporated adequately in computer simulations in order to avoid artifacts. In this work, an MPI-Fortran 90 parallel implementation of Coulombic interactions using the Angular Averaged Ewald sums in Brownian dynamics is reported. This computational implementation is considerably faster than the corresponding serial version for a small to a sizable number of particles (tens of thousands). The accuracy of the parallelized Angular Averaged Ewald sums is compared regarding the Ewald sums method at the level of structural and electrostatic properties of a size- and valence-asymmetric electrolyte.