  Certain simplicial complexes are used to construct a subset $D$ of
$\mathbb{F}_{2^n}^m$ and $D$, in turn, defines the linear code $C_{D}$ over
$\mathbb{F}_{2^n}$ that consists of $(v\cdot d)_{d\in D}$ for $v\in
\mathbb{F}_{2^n}^m$. Here we deal with the case $n=3$, that is, when $C_{D}$ is
an octanary code. We establish a relation between $C_{D}$ and its binary
subfield code $C_{D}^{(2)}$ with the help of a generator matrix. For a given
length and dimension, a code is called distance optimal if it has the highest
possible distance. With respect to the Griesmer bound, five infinite families
of distance optimal codes are obtained, and sufficient conditions for certain
linear codes to be minimal are established.
