We use aMC@NLO to study the production of four charged leptons at the LHC, performing parton showers with both HERWIG and PYTHIA6. Our underlying matrix element calculation features the full next-to-leading order O(alpha(S)) result and the O(alpha(2)(S)) contribution of the gg channel, and it includes all off-shell, spin-correlation, virtual-photon-exchange, and interference effects. We present several key distributions together with the corresponding theoretical uncertainties. These are obtained through a process-independent technique that allows aMC@NLO to compute scale and PDF uncertainties in a fully automated way and at no extra CPU-time cost.