Deviations from the expected two-pion effective-mass distributions have been found in the reaction p̄+p-->2π++2π-+nπ0. These occur in two regions, 300 Mev and 750 Mev, and could be explained by the T=0, pion-pion interaction reported by Abashian, Booth, and Crowe and the widely observed ρ meson (T=1, J=1- pion-pion resonance). The data in the 750-Mev region for π+π- combinations (Q=0) show an apparent double-peak structure-one at 720 Mev (Γ=20 Mev), the other at 780 Mev (Γ=60 Mev). However, the |Q|=1 data (π+π0 and π-π0 combinations) are consistent with the previously observed single T=1, J=1- resonance. Our data give Mρ=767 Mev (Γ=110 Mev). As these parameters also fit the Q=0 data, a detailed discussion of the statistical significance of the one-peak and two-peak hypotheses is given. A search has been made for possible neutral modes of decay of the heavy mesons, and no evidence has been found.