[en] The result of search and investigation of the narrow resonances with isotopic spin I = 2 in the effective mass spectrum of ppπ⁺-combinations from the reaction np → ppπ⁺π^-π^- at P_n = 5.20 ± 0.13 GeV/c are presented. The experimental data were obtained in an exposure of the 1-m H₂ bubble chamber of LHE JINR by monochromatic neutrons. Narrow enhancements were found in the effective mass spectrum of ppπ⁺-combinations at the values for 2175, 2221, 2321, 2398, 2471, 2525, 2596, and 2709 MeV/C². The full experimental widths of the resonances are mainly due to the apparature resolution. There were determined the probabilities of the decay modes for the resonance at the mass of 2596 MeV/c²: into → Δ₃₃⁺⁺p with the probability of (83 ± 23)%, into → (BB)₂₀₉₅⁺⁺π⁺ with the probability of (10 ± 3)%, and into → ppπ⁺ with the probability of (7_-7⁺¹⁵)%. Here, (BB)₂₀₉₅⁺⁺ is the dibaryon in the pp-system near the mass of 2095 MeV/c². Qualitative estimations of the spins were made for the resonances at the masses 2595 and 2709 MeV/c²