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We report on the strong enhancement of vortex pinning in the 115K-superconductor (Cu,C)Ba₂Ca₃Cu₄O_11+d following irradiation with 6 MeV protons. While T_c decreases by only ~2K after doses of up to 10¹⁷ p/cm², the critical current density J_c is enhanced by a factor of 40 in fields above 2 Tesla and at temperatures above 60 K, matching well the range of intended applications. We estimate J_c from magnetization hysteresis measurements on polycrystalline samples using the Bean model. The whole-sample J_c values, deduced by using the sample size as dimension in Bean’s model, approach 5000 A/cm² at 77 K and 1 T. These values are comparable to those of grain-aligned YBa₂Cu₃O_x intended for trapped-field magnets, underlining the application potential of this material if produced for instance in film form. The evolution of the field dependence of J_c with irradiation dose is consistent with a model of strong pinning by large-size inclusions.