A systematic study implementing numerical analysis has been presented in this work in order to design a hexagonal lattice dual core photonic crystal fiber (DC-PCF) which will be simple to fabricate but possesses very good values of optical properties for supercontinuum generation (SCG). By utilizing a full vectoral finite element method with perfectly matched boundary conditions, important propagation properties are numerically evaluated and tuned to desired value through the optimization of structural parameters. Finally, it is found that the optimized PCF structure exhibits very low confinement loss, high birefringence, large effective mode area while maintaining negative chromatic dispersion of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-$</tex-math></inline-formula> 8.3138 ps/km.nm pumping at 1060 nm wavelength. The fiber when excited by a hyperbolic secant pulse having a full-width at half-maximum (FWHM) of 50 fs and a relatively low energy of 4 nJ generates a SC spectrum spanning 600 nm to 1600 nm. The effect of altering the pump power and other parameters on the generated spectra is also explored. Furthermore, the input noise effects on generated SCs have been analyzed through the inclusion of different types of noise. It is found that the generated SC demonstrates excellent coherence property over the entire band extended from visible to the near-IR region and thus it may find applications in lasing, biological imaging, and telecommunication.