The current-driven motion of magnetic domain walls (DWs) is the working principle of magnetic racetrack memories. In this type of spintronic technology, high current densities are used to propel DW motion in magnetic nanowires, causing significant wire heating that corresponds to wasted energy. Synthetic antiferromagnets are known to show very fast DW motion at high current densities, but lower current densities around onset of motion have received less attention. Here we use scanning transmission x-ray microscopy to study the response of DWs in a SAF multilayer to short current pulses. We observe that the DWs depin at $(3.5 \pm 0.4) \times 10^{11}$~A/m$^2$ and move more quickly in response to 5~ns duration current pulses than in comparable multilayers that lack antiferromagnetic coupling. The results suggest that DWs in SAF structures are superior to conventional N'{e}el DWs for low energy consumption racetrack technologies.