A high-temperature (HT) superconducting transition around 120 K and enhanced T_c (R=0) were obtained in bulk polycrystalline Bi_1.6Pb_0.4Sr₂Ca₁Cu₂O_8+x samples. In order to understand the physical origin of the HT transition, different studies such as (i) XRD, TEM/SAD, SEM and EDAX and (ii) effects of post-sintering treatments in O₂ and Na atmospheres and Ca-excess incorporation have been carried out. From all the structural, microstructural and compositional studies, it appears that the major superconducting bulk consists of Bi-2212 phase without any noticeable amount/intergrowth of the most expected second phase (e.g. Bi-2223) in the sample. Moreover, observed behaviours, which are not expected from the Bi-2223 phase, such as displacement of the HT transition and change in T_c (R=0) value towards (i) high-temperature side on N₂ and (ii) lower temperature side on O₂ annealing and on Ca-excess incorporation suggest that both the HT transition and enhanced T_c (R=0) are not because of any Bi-2223 phase and on the contrary indicate that they are due to the low-T_c Bi-2212 phase. In addition, the increase in the commensurate modulation periodicity observed from SAD studies suggests that the increase in the order due to an ordered arrangement of oxygen vacancies has resulted in T_c enhancement of the Bi-2212 phase.