First exclusive data for the $pp to nnpi^+pi^+$ reaction have been obtained at CELSIUS with the WASA detector setup at a beam energy of $T_p$ = 1.1 GeV. Total and differential cross sections disagree with theoretical calculations, which predict the $DeltaDelta$ excitation to be the dominant process at this beam energy. Instead the data require the excitation of a higher-lying $Delta$ state, most likely the $Delta(1600)$, to be the leading process.