With antiprotons stopped in liquid deuterium, the p̄n annihilation channel π−π0η was studied using a final sample of 52 576 events obtained for a spectator proton momentum < 100 MeV/c. In the intensity distribution the ηπ P-wave is clearly apparent by its interferences with the dominant ρ−(770) and a2(1320) two-meson resonances. A partial wave analysis of the data yields evidence for resonant behaviour of the ηπ P-wave, which has the non-qq̄ quantum numbers IG=1−, JPC=1−+. The extracted Breit-Wigner resonance parameters are m=(1400±20±20) MeV/c2 and Γ=(310±50+50−30) MeV/c2.