We report the detection of a Broad Absorption Line (BAL) outflow in the spectrum of the z_em (Mg II) = 2.201 QSO Tol 1037-2703 with three main BALs at 36 000, 25 300 and 22 300 km s-1 outflow velocities. Although the overall flow is dominated by high ionization lines like N V and C IV, the gas of highest velocity shows absorption from Mg I, Mg II and Fe II. Covering factor arguments suggest that the absorbing complexes are physically associated with the QSO and have transverse dimensions smaller than that of the UV continuum emitting region (r < 0.1 pc). We show that the C IV absorption at z_abs = 2.082 has a covering factor f_c ~ 0.86 and the absorption profile has varied over the last four years. The detection of absorption from excited fine structure levels of C II and Si II in narrow components embedded in the C IV trough reveals large density inhomogeneities. IR pumping is the most likely excitation process. The z_abs = 2.139 system is a moderately damped Lyman-α system with log N(H I) ~ 19.7. The weakness of the metal lines together with the high quality of the data make the metallicity measurements particularly reliable. The absolute metallicity is close to solar with [Zn/H] = -0.26. The α-chain elements have metallicities consistently solar (respectively +0.05, -0.02, -0.03 and -0.15 for [Mg/H], [Si/H], [P/H] and [S/H]) and iron peak elements are depleted by a factor of about two ([Fe/Zn], [Cr/Zn], [Mn/Zn] and [Ni/Zn] are equal to -0.39, -0.27, -0.49, -0.30). Lines from C I are detected but H2 is absent with a molecular to neutral hydrogen fraction less than 8x10^-6. From the ionization state of the gas, we argue that the system is situated ~few Mpc away from the QSO. High metallicity and low nitrogen abundance, [N/Zn] = -1.40, favor the idea that metals have been released by massive stars during a starburst of less than 0.5 Gyr of age. Using the upper limit on the C I * column density in two components, we obtain upper limits on the background temperature of 16.2 and 13.2 K respectively.