The uniformly packed binary [27,21,3] and [35,29,3] codes

All binary projective two-weight codes with parameters [27,6,12] and [35,6,16] are enumerated up to equivalence, and the automorphism groups of the codes and related strongly regular graphs computed. Alternatively, this implies the enumeration of all linear binary uniformly packed codes with parameters [27,21,3] and [35,29,3] as dual codes of two-weight codes.