We demonstrate a multi-watt, picosecond pulse duration laser source by exploiting a cascaded Raman process to the second Stokes signal at a wavelength of 2.58 μm in a methane-filled Nested Anti-Resonant Nodeless fiber from a 1 μm disk laser source. A maximum average power of 2.89 W (14.45 μJ) is produced in a 160 cm length of custom-designed and in-house fabricated fiber filled with methane at a pressure of 2 bar. The impact of gas pressure and propagation distance on the second Stokes signal power are investigated experimentally. The experimental results are simulated by solving the Generalized Nonlinear Schrodinger Equation with the experiment carefully modelled by accounting for the impacts of pressure dependent gas-light interactions along the pressure gradient of the fiber. This work offers a laser source for a variety of applications as well as expanding the modelling space to methane filled fibers including pressure gradients, and nonlinear optical activity in the presence of infrared gas absorption.