High-capacity, long-haul transmission over a coupled-core three-core multi-core fiber is investigated in a recirculating loop experiment. We report key system characteristics, such as the optimum launch power as well as the wavelength dependence and distance-evolution of mode-dependent loss and the impulse response time spread. We further performed two high data-rate, long-haul transmission demonstrations with more than 75 nm optical bandwidth in C- and L-bands over distances up to 4800 km. The reported data-rate of 172 Tb/s over 2040 km is the highest demonstrated in any multi-span transmission system employing optical fibers with standard cladding diameter of 125 micro-meter to date. Additionally, transmission of 81 Tb/s over 4800 km distance demonstrates the potential of using coupled-core multi-core fibers in combination with wideband optical signals over long-haul distances.