Highly ordered D2O ice XIV is identified as a possible new candidate phase for ice XX (PNP-ice XX) on the basis of calorimetry, dielectric relaxation spectroscopy, powder X-ray diffraction, and volumetric measurements. Previous work yielded weakly ordered deuterated ice XIV featuring less than 20% of the maximum order defined in terms of Pauling's configurational entropy. Here, we introduce a preparation protocol that allows for highly ordered ice XIV, with a degree of order between 40% and 65%. This protocol involves 110 minutes of annealing of doped ice XII at 94 K and 0.81 GPa, followed by recovery to ambient pressure and storage in liquid nitrogen. The use of both DCl-doping to produce ionic and Bjerrum defects as well as the addition of 1% H2O to produce dynamic H-defects in the bath of D-atoms are key for accelerating the ordering process. At 94 K the dielectric relaxation of highly ordered ice XIV is about ten times slower than that of weakly ordered ice XIV. By contrast to weakly ordered ice XIV, the dielectric relaxation times of highly ordered D2O ice XIV feature a clear kink near the transition to ice XII at 102 K. Furthermore, the volume changes by about 0.6% at the transition of ice XII to ice XIV, owing to the impact of H-ordering on the O-atom network. Powder X-ray diffraction on highly ordered D2O ice XIV reveals several Bragg peaks splittings that are not resolved in weakly ordered ice XIV. These superstructure reflections indicate the presence of a new crystallographic phase and call for powder neutron-diffraction studies to fully elucidate the crystal structure of highly ordered ice XIV.