  In this work, we introduce a new family of [[6k, 2k, 2]] codes designed
specifically to be compatible with adiabatic quantum computation. These codes
support computationally universal sets of weight-two logical operators and are
particularly well-suited for implementing dynamical decoupling error
suppression. For Hamiltonians embeddable on a planar graph of fixed degree, our
encoding maintains a planar connectivity graph and increase the graph degree by
only two. These codes are the first known to possess these features.
