We present a calculation of the next-to-leading order QCD corrections to the hadroproduction process gg → ZZ → e þ e − μ þ μ − , matched to the parton shower in the POWHEG framework. We take advantage of the POWHEG BOX tool for the implementation and rely on PYTHIA8 for the showering and hadronization stages. We fully include γ Ã =Z interference effects, while also covering the single-resonant region. For this phenomenological study we focus on four lepton production as a signal process, neglecting all quark mass effects as well as the Higgs-mediated contributions, which are known to be subdominant in this case. We provide predictions from our simulations for the 13 TeV LHC Run II setup, including realistic experimental cuts.