Data rates in optical fiber networks have increased exponentially over the past decades and core-networks are expected to operate in the peta-bit-per-second regime by 2030. As current single-mode fiber-based transmission systems are reaching their capacity limits, space-division multiplexing has been investigated as a means to increase the per-fiber capacity. Of all space-division multiplexing fibers proposed to date, multi-mode fibers have the highest spatial channel density, as signals traveling in orthogonal fiber modes share the same fiber-core. By combining a high mode-count multi-mode fiber with wideband wavelength-division multiplexing, we report a peta-bit-per-second class transmission demonstration in multi-mode fibers. This was enabled by combining three key technologies: a wideband optical comb-based transmitter to generate highly spectral efficient 64-quadrature-amplitude modulated signals between 1528 nm and 1610 nm wavelength, a broadband mode-multiplexer, based on multi-plane light conversion, and a 15-mode multi-mode fiber with optimized transmission characteristics for wideband operation.