We report on spin injection into a high mobility 2D electron system confined at an (Al, Ga)As/GaAs interface, using (Ga, Mn) As Esaki diode contacts as spin aligners. We measured a clear nonlocal spin valve signal, which varies nonmonotonically with the applied bias voltage. The magnitude of the signal cannot be described by the standard spin drift-diffusion model, because at maximum this would require the spin polarization of the injected current to be much larger than 100%, which is unphysical. A strong correlation of the spin signal with contact width and electron mean free path suggests that ballistic transport in the 2D region below ferromagnetic contacts should be taken into account to fully describe the results.