  In this paper, Algebraic-Geometric (AG) codes and quantum codes associated to
a family of curves which comprises the famous Suzuki curve are investigated.
The Weierstrass semigroup at some rational point is computed. Notably, each
curve in the family turn out to be a Castle curve over some finite field, and a
weak Castle curve over its extensions. This is a relevant feature when codes
constructed from the curve are considered.
