We consider the problem of unsourced random access (U-RA), a grant-free uncoordinated form of random access, in a wireless channel with a massive MIMO base station equipped with a large number $M$ of antennas and a large number of wireless single-antenna devices (users). We consider a block fading channel model where the $M$-dimensional channel vector of each user remains constant over a coherence block containing $L$ signal dimensions in time-frequency. In the considered setting, the number of potential users $K_\text{tot}$ is much larger than $L$ but at each time slot only $K_a \ll K_\text{tot}$ of them are active. Previous results, based on compressed sensing, require that $K_a < L$, which is a bottleneck in massive deployment scenarios such as Internet-of-Things and U-RA. In the context of activity detection it is known that such a limitation can be overcome when the number of base station antennas $M$ is sufficiently large and a covariance based recovery algorithm is employed at the receiver. We show that, in the context of U-RA, the same concept allows to achieve high spectral efficiencies in the order of $\mathcal{O}(L \log L)$, although at an exponentially growing complexity. We show also that a concatenated coding scheme can be used to reduce the complexity to an acceptable level while still achieving total spectral efficiencies in the order of $\mathcal{O}(L/\log L)$.