  We describe the classification of orthogonal arrays OA$(2048,14,2,7)$, or,
equivalently, completely regular $\{14;2\}$-codes in the $14$-cube ($30848$
equivalence classes). In particular, we find that there is exactly one
almost-OA$(2048,14,2,7{+}1)$, up to equivalence. As derived objects,
OA$(1024,13,2,6)$ ($202917$ classes) and completely regular $\{12,2;2,12\}$-
and $\{14, 12, 2; 2, 12, 14\}$-codes in the $13$- and $14$-cubes, respectively,
are also classified.
  Keywords: binary orthogonal array, completely regular code, binary 1-perfect
code.
