Swift J1357.2-0933 is one of the shortest orbital period black hole X-ray transients. It exhibited deep optical dips together with an extremely broad H α line during outburst. We present 10.4-m Gran Telescopio Canarias (GTC) time-resolved spectroscopy during quiescence searching for donor star absorption features. The large contribution of the accretion flow to the total luminosity prevents the direct detection of the companion. Nevertheless, we constrain the non-stellar contribution to be larger than ˜80 per cent of the total optical light, which sets new lower limits to the distance (d > 2.29 kpc) and the height over the Galactic plane (z > 1.75 kpc). This places the system in the Galactic thick disc. We measure a modulation in the centroid of the H α line with a period of P = 0.11 ± 0.04 d which, combined with the recently presented full width at half-maximum-K2 correlation, results in a massive black hole (M1 > 9.3 M⊙) and an ˜M2V companion star (M2 ˜ 0.4 M⊙). We also present further evidence supporting a very high orbital inclination (i ≳ 80°).