We study the production of vector resonances at the LHC via WZ scattering processes and explore the sensitivities to these resonances for the expected future LHC luminosities. The electroweak chiral Lagrangian and the Inverse Amplitude Method (IAM) are used for analyzing a dynamically generated vector resonance, whose origin would be the (hypothetically strong) self interactions of the longitudinal gauge bosons, WL and ZL. We implement the unitarized scattering amplitudes into a single model, the IAM-MC, that as been adapted to MadGraph 5. It is written in terms of the electroweak chiral Lagrangian and an additional effective Proca Lagrangian for the vector resonances, so that it reproduces the resonant behavior of the IAM and allows us to perform a realistic study of signal versus background at the LHC. We focus on the pp→WZjj channel, discussing first on the potential of the hadronic and semileptonic channels of the final WZ, and next exploring in more detail the clearest signals. These are provided by the leptonic decays of the gauge bosons, leading to a final state with l+1l-1l+2νjj, l=e,μ, having a very distinctive signature, and showing clearly the emergence of the resonances with masses in the range of 1.5-2.5 TeV, which we have explored.