  We investigate the problem of percolation of words in a random environment.
To each vertex, we independently assign a letter $0$ or $1$ according to
Bernoulli r.v.'s with parameter $p$. The environment is the resulting graph
obtained from an independent long-range bond percolation configuration on
$\mathbb{Z}^{d-1} \times \mathbb{Z}$, $d\geq 3$, where each edge parallel to
$\mathbb{Z}^{d-1}$ has length one and is open with probability $\epsilon$,
while edges of length $n$ parallel to $\mathbb{Z}$ are open with probability
$p_n$. We prove that if the sum of $p_n$ diverges, then for any $\epsilon$ and
$p$, there is a $K$ such that all words are seen from the origin with
probability close to $1$, even if all connections with length larger than $K$
are suppressed.
