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The propagation of spin waves in single and multilayered ferromagnetic Co-Ta-Zr films is experimentally investigated in this work. Two microstrip antennas placed on top of the magnetic core are used for signal transmission and reception. A metallic ground layer placed on one side of the magnetic film leads to nonreciprocal spin wave dispersion, resulting in a direction-dependent coupling of the antennas. Compared to previous experiments with Ni-Fe films, the higher resistivity of the Co-Ta-Zr reduces the energy dissipation in the device and allows for the incorporation of a thicker magnetic film, thereby increasing the nonreciprocity and the spin wave propagation frequency range. In the case of the Co-Ta-Zr/SiO2 multilayer, the spin wave-mediated coupling of the antennas is strongly dependent on the relative orientation of the magnetizations in the individual layers, and on the application of an external magnetic field.