We report on electrical spin injection from (Ga,Mn)As into a high-mobility two-dimensional electron gas confined at an (Al,Ga)As/GaAs interface. Besides standard nonlocal electrical detection, we use a magneto-optical approach which provides cross-sectional images of the spin accumulation at the cleaved edge of the sample, yielding spin decay lengths on the order of $2\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$. In some cases we find a nonmonotonic bias voltage dependence of the spin signal, which may be linked to ballistic tunneling effects during spin injection. We observe a clear Hanle depolarization using a technique which is free of dynamic nuclear polarization effects. Fitting the data with the standard drift-diffusion model of spin injection suggests averaged in-plane spin lifetimes on the order of 1 ns.