Various theoretical calculations based on QCD or hadronic interactions predict that in addition to the recently observed dibaryon resonance d⁎(2380) with I(JP)=0(3+) there should also exist a dibaryon resonance with mirrored quantum numbers I(JP)=3(0+). We report here on a search for such a NN-decoupled state in data on the pp→ppπ+π+π−π− reaction. Since no clear-cut evidence has been found, we give upper limits for the production cross section of such a resonance in the mass range 2280–2500 MeV. Keywords: Dibaryons, Four-pion production