Brightest cluster galaxies (BCGs) at the centers of clusters are among the most massive galaxies in the Universe. Their star formation history and stellar mass assembly are highly debated. Recent studies suggest the presence of an emerging population of intermediate-z star-forming and gas-rich BCGs, whose molecular gas reservoirs that feed star formation might be impacted by strong environmental processing. We have selected three of the most strongly star-forming z~0.4 BCGs in the equatorial field of the Kilo-Degree Survey (KiDS) and observed them with the IRAM 30m telescope in the first three CO transitions. We found clear double-horn CO(1-->0) and CO(3-->2) emission for the KiDS 1433 BCG, yielding a large molecular gas reservoir with M_H2_=(5.9+/-1.2)10^10^M_{sun}_ and a high gas-to-stellar mass ratio M_H2_/M*=(0.32^+0.12^_-0.10_). We thus increase the still limited sample of distant BCGs with detections in multiple CO transitions. The double-horn emission for the KiDS 1433 BCG implies a low gas concentration, while a modeling of the spectra yields an extended molecular gas reservoir, with a characteristic radius of (5-7) kpc, which is reminiscent of the mature extended-disk phase that is observed in some local BCGs. For the remaining two BCGs, we are able to set robust upper limits of M_H2_/M*<0.07 and <0.23, which are among the lowest for distant BCGs.We then combined our observations with available stellar, star formation, and dust properties of the targeted BCGs, and compared them with a sample of ~100 distant cluster galaxies, including additional intermediate-z BCGs, with observations in CO from the literature. Altogether, our analysis shows that the molecular gas properties of star-forming BCGs are heterogeneous. On the one hand, gas-rich BCGs show extended gas reservoirs that sustain the significant star formation activity, but the efficiency is low, which is reminiscent of recent gas infall. On the other hand, the existence of similarly star forming but gas-poor BCGs suggests that gas depletion precedes star formation quenching.