We performed large-scale simulations in the current-driven three-dimensional frustrated anisotropic XY model in the presense of point-like defects with resistively-shunted junction dynamics. A moving Bragg (BrG) glass is observed applying the current in the equilibrium BrG state. The first-order phase transition from the moving BrG to the moving smectic is clarified. The effect of disorder become weak once the vortex matter is set in motion.