  This paper aims to construct optimal quaternary additive codes with
non-integer dimensions. Firstly, we propose combinatorial constructions of
quaternary additive constant-weight codes, alongside additive anticode
construction. Subsequently, we propose generalized Construction X, which
facilitates the construction of non-integer dimensional optimal additive codes
from linear codes. Then, we construct ten classes of optimal quaternary
non-integer dimensional additive codes through these two methods. As an
application, we also determine the optimal additive $[n,3.5,n-t]_4$ codes for
all $t$ with variable $n$, except for $t=6,7,12$.
