High power diffraction-limited 1064 nm fiber lasers operating in the nanosecond regime can be used for long-range LIDAR and micromachining applications. Peak power is limited by non-linearities, there is therefore an interest to develop fibers exhibiting a very large mode field effective area. New fibers are being developed in the frame of the 4F consortium ("French laser Fibers for Factories of the Future") to fulfill this need. We report on results obtained with a new 39 μm core diameter polarization maintaining ytterbium doped fiber that has been manufactured using the powder sintering technology. It features a large cladding absorption close to 20 dB/m at 976 nm (small signal) and a mode field diameter close to 32 μm. We built a pulsed MOPA. The preamplifier generates 2.5 ns pulses at 1064 nm with 8.5 W average power at 1 MHz pulse repetition frequency. The power amplifier is based on the 39 μm core fiber with 215/230μm hexagonal cladding counterpumped at 976 nm. It features 72 % slope efficiency delivering 72.2 W average power at a pulse repetition rate of 1 MHz. An end-cap was spliced to the fiber output to increase the damage threshold. At 100 kHz a peak power of 351 kW was measured for an average power of 59.9 W. The efficiency is then 70 %. We also studied the influence of the bending radius on the slope efficiency. We do not observe any slope efficiency reduction down to 25 cm bending diameter. It decreased to 68 % for the 20 cm bending diameter. The laser shows a quasisinglemode output beam with a good quality factor M2 of 1.2.