  We study the effects of disorder in a one-dimensional model of
$\mathbb{Z}_{3}$ Fock parafermions which can be viewed as a generalization of
the prototypical Kitaev chain. Exact diagonalization is employed to determine
level statistics, participation ratios, and the dynamics of domain walls. This
allows us to identify ergodic as well as finite-size localized phases. In order
to distinguish Anderson from many-body localization, we calculate the time
evolution of the entanglement entropy in random initial states using tensor
networks. We demonstrate that a purely quadratic parafermion model does not
feature Anderson but many-body localization due to the nontrivial statistics of
the particles.
