We experimentally demonstrate and investigate, for first time to our best knowledge, a second-order few-mode Raman amplifier for low noise distributed fiber amplification. The 1455 and 1360 nm pumps are both injected into the few-mode fiber (FMF) in the forms of two degenerate LP11 modes in the backward direction. Within the band from 1542 to 1558 nm, maximum on-off gains of 4 dB are achieved for both LP01 and LP11 modes, and the differential modal gain (DMG) is less than 0.4 dB. The noise figure (NF) improvements at 1550 nm for LP01 and LP11 modes are 1.2 dB and 1.1 dB, respectively, compared with the conventional first-order pumping scheme. The lowest NFs of less than -2 dB are achieved for both modes. We build an optical time-domain reflectometer (OTDR) in the few-mode distributed Raman amplifier (FM-DRA) to measure the signal evolutions, and the results indicate a proof-of-concept low noise amplification for second-order pumping with respect to the conventional first-order pumping case. Due to the second-order pumping, broadened Raman amplification band has been observed with improved gain flatness for both LP01 and LP11 modes, which is also of great importance in the optical communication systems. The second-order FM-DRA can be used potentially in future high capacity mode-division multiplexing (MDM) optical communication systems.