  Baryogenesis in the context of the compact $SU\left( 3\right)_C\otimes
SU\left( 4\right)_{L}\otimes U\left( 1\right)_X$ model is investigated. Using
the finite temperature effective potential approach together with unitarity,
stability and no ghost masses constraints, the existence of a strong first
order electroweak phase transition (EWPT) was shown and checked numerically
during all steps of the spontaneous breakdown of the gauge symmetry of the
model. Higgs masses regions fulfilling the EWPT criteria are also discussed.
Moreover, and as a byproduct of our study, the B-violation via sphaleron was
also emphasized.
