Context. The Mg II h&k lines are key diagnostics of the solar chromosphere. They are sensitive to the temperature, density, and nonthermal velocities in the chromosphere. The average Mg II h&k line profiles arising from previous 3D chromospheric simulations are too narrow compared to observations. Aims. We study the formation and properties of the Mg II h&k lines in a model atmosphere. We also compare the average spectrum, peak intensity, and peak separation of Mg II k with a representative observation taken by the Interface Region Imaging Spectrograph (IRIS). Methods. We use a model based on the recently developed nonequilibrium version of the radiative magneto-hydrodynamics code MURaM, the MURaM Chromospheric Extension (MURaM-ChE), in combination with forward modeling using the radiative transfer code RH1.5D to obtain synthetic spectra. Our model resembles an enhanced network region created using an evolved MURaM quiet Sun simulation and adding an imposed large-scale bipolar magnetic field similar to that in the public Bifrost snapshot of a bipolar magnetic feature. Results. The line width and the peak separation of the spatially averaged spectrum of the Mg II h&k lines from the MURaM-ChE simulation are close to a representative observation of the quiet Sun, which also includes network fields. However, we find the synthesized line width to be still slightly narrower than in the observation. We find that velocities in the chromosphere play a dominant role in the broadening of the spectral lines. While the average synthetic spectrum also shows a good match to the observations in the pseudo continuum between the two emission lines, the peak intensities are higher in the modeled spectrum. This discrepancy may be due in part to the larger magnetic flux density in the simulation than in the considered observations, but could also be a result of the 1.5D radiative transfer approximation. Conclusions. Our findings show that strong maximum-velocity differences or turbulent velocities in the chromosphere and lower atmosphere are necessary to reproduce the observed line widths of chromospheric spectral lines.