High-average power, ultra-broadband, mid-IR radiation can be generated in a nonlinear medium by illuminating it with a multi-line laser radiation. Propagation of a multi-line CO2 laser beam in a nonlinear medium, e.g. gallium arsenide or chalcogenide, will generate directed, broadband, IR radiation in the atmospheric window (2-13 μm). A 3-D laser code for propagation in a nonlinear medium has been developed to incorporate extreme spectral broadening resulting from the beating of several wavelengths. The code has the capability to treat coupled forward and backward propagating waves. In addition, we include transverse and full linear dispersion effects. Methods for enhancing the spectral broadening are proposed and analyzed; in particular, grading the refractive index radially will tend to guide the CO2 radiation and extend the interaction distance, allowing for enhanced spectral broadening. Finally, we show that the laser phase noise associated with the finite CO2 linewidths can significantly enhance the spectral broadening. In a dispersive medium laser phase noise results in laser intensity fluctuations. These intensity fluctuations result in spectral broadening due to the self-phase modulation mechanism.