The newly developed ϕ6 - Model expansion method has been successfully applied in this article for locating several new exact solutions including Jacobi elliptic solutions, solitons and other solutions to the coupled system of NLSE with QC nonlinearity that models birefringence. The soliton solutions that are recovered in this article are been reported for the first time. The effect of 4WM was taken into account and consequently phase- matching condition has been implemented to secure these soliton solutions. Our results show extreme promise with the methodology applied to such model. The results will, in future, be applied to additional optoelectronic devices as will as optoelectronic phenomena and these include DWDM networks, highly dispersive solitons, meta-optics and other such devices. The results of those research activities are currently awaited, but not for long!!