  In this work, we provide new examples of Anti-de Sitter black holes with a
planar base manifold in four-dimensional Critical Gravity by considering
nonlinear electrodynamics as a matter source. We find a general solution
characterized by the presence of only one integration constant where, for a
suitable election of coupling constants, we can show the existence of one or
more horizons. Additionally, we compute its non-null thermodynamical quantities
through a variety of techniques, testing the validity of the first law of
thermodynamics as well as a Smarr formula. Finally, we analyze the local
thermodynamical stability of the solutions. To our knowledge, these charged
configurations are the first example with Critical Gravity where their
thermodynamical quantities are not zero.
