The running axial mass model (MArun) is a phenomenological model for describing charged-current quasielastic (CCQE or 1p1h) and meson exchange current (MEC or 2p2h) neutrino--nucleus interactions with two universal parameters. We test its implementation in GENIE v3.4.0 against the inclusive $\nu_\mu$ charged-current cross section measured in the NOvA near detector. The calculation takes into account the actual target composition and neutrino flux of the NOvA near detector (ND), while the MArun parameters are kept fixed at the values obtained from previous global fit to accelerator data. The measured inclusive double-differential cross section $d^2\sigma/d\cos\theta_\mu dT_\mu$ is compared with the simulation, including 1p1h, 2p2h, resonance (RES), and deep inelastic (DIS) contributions. The MArun prediction reproduces the main features of the measured cross section over most of the measured phase space. A quantitative comparison using the full NOvA covariance matrix gives an overall normalization factor of $N\simeq1.11$, compatible with the quoted $11.2\%$ normalization uncertainty. The results show that MArun provides a consistent description of the NOvA near-detector data without any tuning of its parameters to this data set.