We present scanning tunneling spectroscopy measurements of the local quasiparticles' excitation spectra of the heavy fermion CeCoIn 5 between 440 mK and 3 K in samples with a bulk T c = 2.25 K. The spectral shape of our low-temperature tunneling data, quite textbook nodal-∆ conductance, allow us to confidently fit the spectra with a dwave density of states considering also a shortening of quasiparticles' lifetime term Γ. The ∆(0) value obtained from the fits yields a BCS ratio 2∆/kT c = 7.73 suggesting that CeCoIn 5 is an unconventional superconductor in the strong coupling limit. The fits also reveal that the height of coherence peaks in CeCoIn 5 is reduced with respect to a pure BCS spectra and therefore the coupling of quasiparticles with spin excitations should play a relevant role. The tunneling conductance shows a depletion at energies smaller than ∆ for temperatures larger than the bulk T c , giving further support to the existence of a pseudogap phase that in our samples span up to T * ∼ 1.2T c . The phenomenological scaling of the pseudogap temperature observed in various families of cuprates, 2∆/kT * ∼ 4.3, is not fulfilled in our measurements. This suggests that in CeCoIn 5 the strong magnetic fluctuations might conspire to close the local superconducting gap at a smaller pesudogap temperature-scale than in cuprates.