  We extend the recently presented, fully exclusive, next-to-leading-order
accurate event generator for the simulation of massless neutral- and
charged-current deep inelastic scattering (DIS) to the case of incoming
neutrinos. The generator can be used to study neutrino-nucleon interactions at
(ultra) high energies, and is relevant for a range of fixed-target collider
experiments and large-volume neutrino detectors, investigating atmospheric and
astrophysical neutrinos. The matching with multi-purpose event generators such
as PYTHIA 8 is performed with the POWHEG method, and accounts for parton
showering and non-perturbative effects such as hadronization. This makes it
possible to investigate higher-order perturbative corrections to realistic
observables, such as the distribution of charged particles. To illustrate the
capabilities of the code we provide predictions for several differential
distributions in fixed-target collisions for neutrino energies up to 1 PeV.
