An Ne-like transient collisional excitation x-ray laser at 19.6 nm (J = 0 1, 3p 3s) was investigated numerically using a sophisticated hydrodynamic code for a 100 µm thick Ge planar target irradiated by a nanosecond pre-pulse followed by a picosecond main optical laser pulse. The simulations indicate that for a given peak intensity, the main pulse has an optimal duration to generate the maximum effective gain. An effective gain as high as 200 cm^-1 was obtained for the optimized drive pulse configuration.