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We present a generator for lepton nucleon collisions in the DIS regime, focusing in particular on processes with a massive lepton and/or a massive quark in the final state. We have built a full code matching NLO QCD corrections to parton shower Monte Carlo programs in the POWHEG-BOX framework. Our code can be used to compute NLO+ PS accurate fully differential predictions for neutral current and charged current processes, including processes with an incoming tau neutrino, and/or including charm quarks in the final state. We also made comparisons with available data and predictions for the new neutrino experiments at CERN.