We report on measurements of critical current densities Jc and flux creep rates S of freestanding Ca(Fe1−xCox)2As2 (x ≈ 0.033) single crystals with Tc ≈ 15.7 K by performing magnetization measurements. The magnetic field dependences of Jc at low temperature display features related to strong pinning. In addition, we find that the system displays small flux creep rates. The characteristic glassy exponent, μ, and the pinning energy, U0, display exceptional high values for pristine crystals. We find that for magnetic fields between 0.3 T and 1 T, μ decreases from ≈ 2.8 to ≈ 2 and U0 remains ≈ 300 K. Analysis of the pinning force indicates that the mechanism is similar to the observed in polycrystalline systems in which grain boundaries and random disorder produce the vortex pinning. Considering the large U0 observed in the single crystal, we attempt to improve the pinning by adding random point disorder by 3 MeV proton irradiation with a fluence of 2 × 1016 proton/cm2. The results show that, unlike other iron-based superconductors, the superconducting fraction is sharply reduced by irradiation. This fact indicates that the superconductivity in the system is extremely fragile to an increment in the disorder. The superconducting volume fraction in the irradiated crystal systematically recovers after removal disorder by thermal annealing, which evidences as to the observation of critical state in curves of magnetization versus magnetic field. No features related to a reentrant antiferromagnetic transition are observed for the irradiated sample.