We report on the demonstration and characterization of Raman laser generating at the wavelength of ~1090 nm with total output power of up to 5 W based on the 7-core passive fiber with coupled cores. The Raman gain in all cores is provided by the pump laser connected to the FBG-free central core, whereas the laser cavity is formed by two sets of highly-reflective fiber Bragg gratings (FBGs) inscribed by fs pulses in all peripherical cores at the both ends of the 7-core fiber. The output FBG set has got a random shift along the axis between individual FBGs thus forming a random array of FBGs. Along with the Stokes line narrowing reasoned by the reduction of spectral broadening via nonlinear effects due to the enlargement of effective mode area in the multicore fiber with coupled cores in comparison with a standard singlemode fiber Raman laser, the additional line narrowing effect induced by the multicore random FBG array has been also revealed. It results in the generation of single peak of <30 pm linewidth near the threshold, whereas the linewidth broadens to ~250 pm at maximum power. At that, the single peak generation at low powers is not stable in time converting at some moments to multiple 20-pm peaks with random spacing and amplitudes defined by the interference of beams reflected from individual output FBGs with random longitudinal shifts. The ways to stabilize the generated spectrum are discussed.