The Brillouin zone spin filtering mechanism of enhanced tunneling magnetoresistance (TMR) is described for magnetic tunnel junctions (MTJs) and studied for an example of the MTJ with hcp Co electrodes and hexagonal BN (h-BN) spacer. Our calculations based on the local density approximation of density-functional theory (LDA-DFT) for Co(0001)/h-BN/Co(0001) MTJ predict high TMR in this device due to Brillouin zone filtering mechanism. Owning to the specific complex band structure of the h-BN the spin-dependent tunneling conductance of the system is ultrasensitive to small variations of the Fermi energy position inside the BN band gap. Doping of the BN and, consequentially, changing the Fermi energy position could lead to variation of the TMR by several orders of magnitude. We show also that taking into account correlation effects on beyond DFT level is required to accurately describe position of the Fermi level and thus transport properties of the system. Our study suggests that new MTJ based on hcp Co-Pt or Co-Pd disordered alloy electrodes and p-doped hexagonal BN spacer is a promising candidate for the spin-transfer torque magnetoresistive random-access memory.