The Benzenoid Generation Problem (BGP) aims at generating all benzenoid molecules that satisfy some given properties. This problem has important applications in chemistry, and Carissan et al (2021) have shown us that Constraint Programming (CP) is well suited for modelling this problem because properties defined by chemists are easy to express by means of constraints. Benzenoids are described by hexagon graphs and a key point for an efficient enumeration of these graphs is to be invariant to rotations and symmetries. In this paper, we introduce canonical codes that uniquely characterise hexagon graphs while being invariant to rotations and symmetries. We show that these codes may be defined by means of constraints. We also introduce a global constraint for ensuring that codes are canonical, and a global constraint for ensuring that a pattern is included in a code. We experimentally compare our new CP model with the CP-based approach of Carissan et al (2021), and we show that it has better scale-up properties.