A triplet code model of leptons and quarks is proposed. Assuming the internal A-spin, B-spin and C-spin of particles, from fundamental symmetry SO(4) the color SU(3), horizontal SU(3), electroweak SU(2) X U(1) and other higher composite symmetries are derived. Using composite symmetry operators, the mass gap between third generation and the first two can be derived. The modification to the standard electrowea.k gauge theory is also discussed in some detail.