  We describe a pair of constructions of Eisenstein lattices from ternary
codes, and a corresponding pair of constructions of conformal field theories
from lattices which turn out to have a string theoretic interpretation. These
are found to interconnect in a similar way to results for binary codes, which
led to a generalisation of the triality structure relevant in the construction
of the Monster module. We therefore make some comments regarding a series of
constructions of $V^\natural$. In addition, we present a complete construction
of the Niemeier lattices from ternary codes, which in view of the above
analogies should prove to be of great importance in the problem of the
classification of self-dual $c=24$ conformal field theories. Other progress
towards this problem is summarised, and some comments arise from this
discussion regarding the uniqueness of the Monster conformal field theory.
(Talk presented at the "Monster Bash", Ohio State University, May 1993.)

High Energy Physics - Theory