The XMM-Newton Distant Cluster Project is a serendipitous survey for clusters of galaxies at redshifts z>=0.8 based on deep archival XMM-Newton observations. ... Low-significance candidate high-z clusters are followed up with the seven-channel imager GROND (Gamma-Ray Burst Optical and Near-Infrared Detector) that is mounted at a 2m-class telescope. ... The test case is XMMU J0338.7+0030, suggested to be at z~1.45+/-0.15 from the analysis of the z-H vs H colour-magnitude diagram obtained from the follow-up imaging. Later VLT-FORS2 spectroscopy enabled us to identify four members, which set this cluster at z=1.097+/-0.002. To reach a better knowledge of its galaxy population, we observed XMMU J0338.7+0030 with GROND for about 6 hr. The publicly available photo-z code le Phare was used. The Ks-band number counts of the non-stellar sources out of the 832 detected down to z~26 AB-mag in the 3.9x4.3 square arcmin region of XMMU J0338.7+0030 imaged at all GROND bands clearly exceed those computed in deep fields/survey areas at ~20.5 - 22.5 AB-mag. The photo-zs of the three imaged spectroscopic members yield z=1.12+/-0.09. The spatial distribution and the properties of the GROND sources with a photo-z in the range 1.01 - 1.23 confirm the correspondence of the X-ray source with a galaxy over-density at a significance of at least 4.3 sigma. Candidate members that are spectro-photometrically classified as elliptical galaxies define a red locus in the i-z vs z colour-magnitude diagram that is consistent with the red sequence of the cluster RDCS J0910+5422 at z=1.106. XMMU J0338.7+0030 hosts also a population of bluer late-type spirals and irregulars. The starbursts among the photometric members populate both loci, consistently with previous results. The analysis of the available data set indicates that XMMU J0338.7+0030 is a low-mass cluster (M_200 ~ 1E14 M_sun) at z=1.1. (Abridged)
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