We demonstrate a narrow-linewidth high-order-mode (HOM) Brillouin random fiber laser (BRFL) based on a long-period fiber grating (LPFG) and distributed Rayleigh random feedback in a half-open linear cavity. The single-mode operation of the laser radiation with sub-kilohertz linewidth is achieved thanks to distributed Brillouin amplification and Rayleigh scattering along kilometer-long single mode fibers whilst a few mode fiber-based LPFGs enable the transverse mode conversion among a broadband wavelength range. Meanwhile, a dynamic fiber grating (DFG) is embedded and incorporated to manipulate and purify the random modes, which hence suppresses the frequency drift resulting from random mode hopping. Consequently, the random laser emission with either high-order scalar or vector modes can be generated with a high laser efficiency of 25.5% and an ultra-narrow 3-dB linewidth of 230 Hz. Furthermore, the dependence of the laser efficiency and frequency stability on the gain fiber length are also experimentally investigated. It is believed that our approach could provide a promising platform for a wide range of applications such as coherent optical communication, high-resolution imaging, highly sensitive sensing, etc.