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We present a novel next-to-next-to-leading order (NNLO) QCD calculation matched to parton shower for the production of a pair of Z bosons decaying to four massless leptons, pp→ℓ+ℓ−ℓ′+ℓ′−+X, at the LHC. Spin correlations, interferences and off-shell effects are included throughout. Our result is based on the resummed beam-thrust spectrum, which we evaluate at next-to-next-to-leading-logarithmic (NNLLT0′) accuracy for the first time for this process, and makes use of the Geneva Monte Carlo framework for the matching to Pythia8 shower and hadronisation models. We compare our predictions with data from the ATLAS and CMS experiments at 13TeV, finding a good agreement.