We report on the design, fabrication, and experimental characterization of germanium-doped graded-index multi-mode fibers that are tailored to achieve broadband operation for the intermodal Bragg scattering four wave mixing process. First, we show that increasing the core diameter decreases the separation between the pumps and the signal/idler pair. Second, we demonstrate a conversion efficiency bandwidth (7 nm) of more than twice that achieved previously with half the fiber length (50 m).