In the present project we apply a 3D MHD numerical model to simulate the evolution of a large-scale magnetic field in a barred galaxy possessing a gaseous halo. A time-dependent velocity field of molecular gas resulting from self-consistent 3D N-body simulations of a galactic disk is used to solve the induction equation. The gaseous halo rotates differentially, co-rotating with the disk. In order to form field structures high above the galactic disk in our model, we introduce the dynamo process causing, as well, the amplification of the magnetic field. The simulated magnetic fields are used to construct the maps of a high-frequency (Faraday rotation-free) polarized radio emission that accounts for effects of projection and limited resolution, and is thus suitable for direct comparison with observations. The magnetic field obtained correctly reproduces the observed structures of polarization B-vectors. They form coherent patterns well aligned with spiral arms and with the bar. We found the dynamical process which initializes a wave-like behavior of the magnetic field efficiently forming magnetic maxima between the spiral arms. The magnetic structures in a form of flux tubes extending along the spiral arms are found, as well.