PKS 1424+240 is a BL-Lac blazar with unknown redshift that was detected at high-energy gamma rays by Fermi-LAT with a hard spectrum. At VHE, it was first detected by VERITAS and later confirmed by MAGIC. Its spectral energy distribution is highly attenuated at VHE gamma rays, which is coherent with distant sources. Several estimations enabled the redshift to be constrained to the range 0.6 < z < 1.3. These results place PKS 1424+240 in the very interesting condition of being probably the most distant blazar that has been detected at VHE. The ambiguity in the redshift is still large enough to prevent precise studies of the EBL and the intrinsic blazar spectrum. Given the difficulty of measuring spectroscopic redshifts for BL-Lac objects directly, we aim to establish a reliable redshift value for this blazar by finding its host group of galaxies. Elliptical galaxies are associated with groups, and BL-Lac objects are typically hosted by them, so we decided to search for the host group of the blazar. For this, we performed optical spectroscopic observations of thirty objects in the field of view of PKS 1424+240 using the Gemini MOS. After analysing the data for groups, we evaluated the probability of finding groups of galaxies by chance around the position of PKS 1424+240, using a deep catalogue of groups. We also used photometric data from the SDSS catalogue to analyse the red sequence of the proposed blazar host group. We found a new group of galaxies with eight members at z = 0.6010 +- 0.003, a virial radius of R_vir = 1.53 Mpc, and a velocity dispersion of sigma_v = 813 +- 187 km/s. The photometric study indicates that more members are probably populating this previously uncatalogued group of galaxies. The probability of PKS 1424+240 being a member of this group was found to be 98%. The new group of galaxies found at z = 0.6010 +- 0.003 is very likely hosting PKS 1424+240.