We report on measurements of baryon resonance and ρ meson production in the exclusive pp → ppπ+π− channel at a beam kinetic energy of 3.5 GeV measured with the HADES experimental setup. The differential distributions are compared to Monte Carlo simulations based on a resonance model assuming an incoherent sum of contributions of various baryonic resonances with masses below 2 GeV and using inputs from one pion production measured in the same experiment. A very good description of the two pion production is achieved allowing for an estimate of the contribution of one and double baryon-resonance excitation. Using appropriate kinematical cuts the ρ meson signal could also be extracted.