We present a stacked weak-lensing analysis of 27 richness selected galaxy clusters at 0.40 <= z <= 0.62 in the COnstrain Dark Energy with X-ray galaxy clusters (CODEX) survey. The fields were observed in five bands with the Canada-France-Hawaii Telescope (CFHT). We measure the stacked surface mass density profile with a 14 sigma significance in the radial range 0.1 < R Mpc h(-1) < 2.5. The profile is well described by the halo model, with the main halo term following a Navarro-Frenk-White profile (NFW) profile and including the off-centring effect. We select the background sample using a conservative colour-magnitude method to reduce the potential systematic errors and contamination by cluster member galaxies. We perform a Bayesian analysis for the stacked profile and constrain the best-fitting NFW parameters M-200c = 6.6(- 0.8)(+1.0) x 10(14) h(-1)M(circle dot) and c(200c) = 3.7(+0.7) (-0.6). The off-centring effect was modelled based on previous observational results found for redMaPPer Sloan Digital Sky Survey clusters. Our constraints on M(200)c and c(200)c allow us to investigate the consistency with numerical predictions and select a concentration-mass relation to describe the high richness CODEX sample. Comparing our best-fitting values forM(200c) and c(200c) with other observational surveys at different redshifts, we find no evidence for evolution in the concentration-mass relation, though it could be mitigated by particular selection functions. Similar to previous studies investigating the X-ray luminosity-mass relation, our data suggest a lower evolution than expected from self-similarity.