  We present a calculation of the next-to-leading order (NLO) QCD corrections
to the hadroproduction process $gg\to ZZ \to e^+e^- \mu^+ \mu^-$, matched to
the parton shower in the POWHEG framework. We take advantage of the POWHEG BOX
tool for the implementation and rely on PYTHIA 8 for the showering and
hadronization stages. We fully include $\gamma^*/Z$ 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.
