  Perfect codes in the $n$-dimensio\-nal grid $\Lambda_n$ of the lattice
$\mathbb{Z}^n$ ($0<n\in\mathbb{Z}$) and its quotient toroidal grids were
obtained via the truncated distance in $\mathbb{Z}^n$ given between
$u=(u_1,\cdots,u_n)$ and $v=(v_1, \ldots,v_n)$ as the graph distance $h(u,v)$
in $\Lambda_n$, if $|u_i-v_i|\le 1$, for all $i\in\{1, \ldots,n\}$, and as
$n+1$, otherwise. Such codes are extended to multilattice graphs $\Gamma_n$
obtained by glueing ternary $n$-cubes along their codimension 1 ternary
subcubes in such a way that each binary $n$-subcube is contained in a unique
maximal lattice of $\Gamma_n$. The existence of an infinite number of isolated
perfect truncated-metric codes of radius 2 in $\Gamma_n$ for $n=2$ is
ascertained, leading to conjecture such existence for $n>2$ with radius $n$.
