A search for a heavy Standard Model Higgs boson decaying via H → Z Z → ℓ+ℓ−q ̄q, where ℓ = e or μ, is presented. The search uses a data set of pp collisions at √s = 7 TeV, corresponding to an integrated luminosity of 4.7 fb−1 collected in 2011 by the ATLAS detector at the CERN LHC. No significant excess of events above the estimated background is found. Upper limits at 95% confidence level on the production cross section of a Higgs boson with a mass in the range between 200 and 600 GeV are derived. A Standard Model Higgs boson with a mass in the range 300 GeV ≼ mH ≼ 322 GeV or 353 GeV ≼ mH ≼ 410 GeV is excluded at 95% CL. The corresponding expected exclusion range is 351 GeV ≼ mH ≼ 404 GeV at 95% CL.