Raman lasing in a graded-index fiber (GIF) attracts now great deal of attention due to the opportunity to convert high-power multimode laser diode radiation into the Stokes wave with beam quality improvement based on the Raman clean-up effect. Here we report on the cascaded Raman generation of the 2nd Stokes order in the 1.1-km long GIF with 100-μm core directly pumped by 915-nm diodes. In the studied all-fiber scheme, the 1st Stokes order is generated at 950-954 nm in a linear cavity formed at GIF ends by two fiber Bragg gratings (FBGs) securing beam quality improvement from M2 ≈ 30 to M2 ≈ 2.3 due to special transverse structure of FBGs. The 2nd Stokes wave is generated either in linear (two FBGs) or half-open (one FBG) cavity with random distributed feedback via Rayleigh backscattering. Their comparison shows that the random lasing provides better beam quality and higher slope efficiency. Nearly diffraction limited beam (M2 ≈ 1.6) with power up to 27 W at maximum gain (996 nm), and 17 W at the detuned wavelength of 978 nm has been obtained, thus demonstrating that the 2nd-order random lasing in diode-pumped GIF with FBGs provides high-efficiency high-quality beam generation in a broad wavelength range within the Raman gain spectral profile.