  For $q,n,d \in \mathbb{N}$, let $A_q^L(n,d)$ denote the maximum cardinality
of a code $C \subseteq \mathbb{Z}_q^n$ with minimum Lee distance at least $d$,
where $\mathbb{Z}_q$ denotes the cyclic group of order $q$. We consider a
semidefinite programming bound based on triples of codewords, which bound can
be computed efficiently using symmetry reductions, resulting in several new
upper bounds on $A_q^L(n,d)$. The technique also yields an upper bound on the
independent set number of the $n$-th strong product power of the circular graph
$C_{d,q}$, which number is related to the Shannon capacity of $C_{d,q}$. Here
$C_{d,q}$ is the graph with vertex set $\mathbb{Z}_q$, in which two vertices
are adjacent if and only if their distance (mod $q$) is strictly less than $d$.
The new bound does not seem to improve significantly over the bound obtained
from Lov\'asz theta-function, except for very small $n$.
