In this Letter, we report on photoconductive terahertz (THz) detectors for 1550 nm excitation based on a low-temperature-grown InGaAs/InAlAs superlattice with a localized beryllium doping profile. With this approach, we address the inherent lifetime-mobility trade-off that arises, since trapping centers also act as scattering sites for photo-excited electrons. The localized doping of the InAlAs barrier only leads to faster electron trapping for a given mobility. As a result, we obtain THz detectors with more than 6 THz bandwidths and 70 dB dynamic ranges (DNRs) at 3 THz and 55 dB DNR at 4 THz. To the best of our knowledge, this is the highest DNR for photoconductive THz time-domain spectroscopy systems published so far.