  In this paper, we mainly study quaternary linear codes and their binary
subfield codes. First we obtain a general explicit relationship between
quaternary linear codes and their binary subfield codes in terms of generator
matrices and defining sets. Second, we construct quaternary linear codes via
simplicial complexes and determine the weight distributions of these codes.
Third, the weight distributions of the binary subfield codes of these
quaternary codes are also computed by employing the general characterization.
Furthermore, we present two infinite families of optimal linear codes with
respect to the Griesmer Bound, and a class of binary almost optimal codes with
respect to the Sphere Packing Bound. We also need to emphasize that we obtain
at least 9 new quaternary linear codes.
