Thick biological tissues give rise to not only the multiple scattering of incoming light waves, but also the aberrations of remaining signal waves. The challenge for existing optical microscopy methods to overcome both problems simultaneously has limited sub-micron spatial resolution imaging to shallow depths. Here we present an optical coherence imaging method that can identify aberrations of waves incident to and reflected from the samples separately, and eliminate such aberrations even in the presence of multiple light scattering. The proposed method records the time-gated complex-field maps of backscattered waves over various illumination channels, and performs a closed-loop optimization of signal waves for both forward and phase-conjugation processes. We demonstrated the enhancement of the Strehl ratio by more than 500 times, an order of magnitude or more improvement over conventional adaptive optics, and achieved a spatial resolution of 600 nm up to an imaging depth of seven scattering mean free paths.