Résumé : A mass-independent partial-wave analysis of the reaction π-p → ηπ0n is performed in the ηπ0 mass range above 1.6 GeV. The analysis employs the S, P, D, F, and G waves and is based on experimental data collected with the GAMS-2000 multiphoton spectrometer in a 38-GeV/c pion beam extracted from the 70-GeV accelerator of IHEP. A resonance with quantum numbers JPC = 4++ and IG = 1- is observed in the G wave. Its mass and width are measured to be M = 2010 ± 20 MeV and Γ = 370 ± 80 MeV. The mechanism of the observed a04-meson production is dominated by natural-spin-parity exchange in the t channel. The measured unnaturalto-natural cross-section ratio is 0.60 ± 0.16.