  Garcia and Stichtenoth discovered two towers of function fields that meet the
Drinfeld-Vl\u{a}du\c{t} bound on the ratio of the number of points to the
genus. For one of these towers, Garcia, Pellikaan and Torres derived a
recursive description of the Weierstrass semigroups associated to a tower of
points on the associated curves. In this article, a non-recursive description
of the semigroups is given and from this the enumeration of each of the
semigroups is derived as well as its inverse. This enables us to find an
explicit formula for the order (Feng-Rao) bound on the minimum distance of the
associated one-point codes.
