  Let $p$ be a prime such that $p \equiv 2$ or $3$ mod $5$. Linear block codes
over the non-commutative matrix ring of $2 \times 2$ matrices over the prime
field $GF(p)$ endowed with the Bachoc weight are derived as isometric images of
linear block codes over the Galois field $GF(p^2)$ endowed with the Hamming
metric. When seen as rank metric codes, this family of matrix codes satisfies
the Singleton bound and thus are maximum rank distance codes, which are then
lifted to form a special class of subspace codes, the Grassmannian codes, that
meet the anticode bound. These so-called anticode-optimal Grassmannian codes
are associated in some way with complete graphs. New examples of these maximum
rank distance codes and anticode-optimal Grassmannian codes are given.
