We present a low-noise distributed acoustic sensor using enhanced backscattering fiber with a series of localized reflectors. The point reflectors were inscribed in a standard telecom fiber in a fully automated system by focusing an ultra-fast laser through the fiber cladding. The inscribed reflectors provided a reflectance of -53 dB, significantly higher than the Rayleigh backscattering level of -70 dB/m, despite adding only 0.01 dB of loss per 100 reflection points. We constructed a coherent φ-OTDR system using a double-pulse architecture to probe the enhanced backscattering fiber. Using this system, we found that the point reflectors enabled an average phase noise of -91 dB (re rad2/Hz), 20 dB lower than sensors formed using Rayleigh backscattering in the same fiber. The sensors are immune to interference fading, exhibit a high degree of linearity, and demonstrate excellent non-local signal suppression (>50 dB). This work illustrates the potential for low-cost enhanced backscattering fiber to enable low-noise, long-range distributed acoustic sensing.