An algorithm based upon the boundary-edges code and the reverse search method is proposed for enumerating non-isomorphic planar simply connected polyhexes. These polyhexes are associated with vertices of a graph whose edges correspond to addition of an hexagon. A directed tree is defined on this graph. To this effect, a new father-son relationship is introduced: the father is the polyhex obtained when removing the hexagon associated with the first digit of the son's code. Then testing if a generated polyhex is a legitimate one in the enumeration can be done easily and efficiently. The resulting algorithm is used to enumerate polyhexes with hexagons, a set of over one trillion molecules, i.e., more than 600 times larger than previously done.