  If the cyclic sequences of {face types} {at} all vertices in a map are the
same, then the map is said to be a semi-equivelar map. In particular, a
semi-equivelar map is equivelar if the faces are the same type. Homological
quantum codes represent a subclass of topological quantum codes. In this
article, we introduce {thirteen} new classes of quantum codes. These codes are
associated with the following: (i) equivelar maps of type $ [k^k]$, (ii)
equivelar maps on the double torus along with the covering of the maps, and
(iii) semi-equivelar maps on the surface of \Echar{-1}, along with {their}
covering maps. The encoding rate of the class of codes associated with the maps
in (i) is such that $ \frac{k}{n}\rightarrow 1 $ as $ n\rightarrow\infty $, and
for the remaining classes of codes, the encoding rate is $
\frac{k}{n}\rightarrow \alpha $ as $ n\rightarrow \infty $ with $ \alpha< 1 $.
