  Using a permutation code introduced by Rakotondrajao and the second author,
we associate with every set partition of $[n]$ a permutation over $[n]$, thus
defining a class of permutation whose size is the $n$-th Bell number. We
characterize the permutations belonging to this class and we study the
distribution of weak exceedances over these permutations, which turns out to be
enumerated by the Stirling numbers of the second kind. We provide a direct
bijection between our class of permutations and another equisized class of
permutations introduced by Poneti and Vajnovszki.
