Brightest cluster galaxies (BCGs) are excellent laboratories for the study of galaxy evolution in dense Mpc-scale environments. We used the IRAM-30 m to observe, in CO(1→0), CO(2→1), CO(3→2), or CO(4→3), 18 BCGs at z ∼ 0.2 − 0.9 drawn from the Cluster Lensing And Supernova survey with Hubble (CLASH) survey. Our sample includes RX1532, which is our primary target as it is among the BCGs with the highest star formation rate (SFR ≳100 M⊙ yr−1) in the CLASH sample. We unambiguously detected both CO(1→0) and CO(3→2) in RX1532, yielding a large reservoir of molecular gas, MH2 = (8.7 ± 1.1)×1010 M⊙, and a high level of excitation, r31 = 0.75 ± 0.12. A morphological analysis of the Hubble Space Telescope I-band image of RX1532 reveals the presence of clumpy substructures both within and outside the half-light radius re = (11.6 ± 0.3) kpc, similarly to those found independently both in ultraviolet and in Hα in previous works. We tentatively detected CO(1→0) or CO(2→1) in four other BCGs, with molecular gas reservoirs in the range of MH2 = 2 × 1010 − 11 M⊙. For the remaining 13 BCGs, we set robust upper limits of MH2/M⋆ ≲ 0.1, which are among the lowest molecular-gas-to-stellar-mass ratios found for distant ellipticals and BCGs. In comparison with distant cluster galaxies observed in CO, our study shows that RX1532 (MH2/M⋆ = 0.40 ± 0.05) belongs to the rare population of star-forming and gas-rich BCGs in the distant universe. By using the available X-ray based estimates of the central intra-cluster medium entropy, we show that the detection of large reservoirs of molecular gas MH2 ≳ 1010 M⊙ in distant BCGs is possible when the two conditions are met: (i) high SFR and (ii) low central entropy, which favors the condensation and the inflow of gas onto the BCGs themselves, similarly to what has been previously found for some local BCGs.Key words: galaxies: clusters: general / galaxies: evolution / galaxies: star formation / galaxies: active / molecular data⋆ The reduced spectra are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/640/A65