We report results of an electron spin resonance (ESR) study of a spin-gap antiferromagnet (C(4)H(12)N(2))(Cu(2(Cl(6)) (nicknamed PHCC) with chlorine ions partially substituted by bromine. We found that up to 10% of nominal doping the contribution of the random defects to the absorption spectra remains at about 0.1% per copper ion, which is almost the same as in the pure system. Instead, a particular kind of ESR absorption corresponding to gapless S = 1 triplets is observed at low temperatures in samples with high nominal bromine content x ≥ 5%. Increase of bromine concentration also leads to the systematic broadening of ESR absorption line, indicating reduction of the quasi-particles lifetime.