Bi-based high-T(c) superconductors of nominal composition Bi2Sr2Ca3Cu4O12+z (n = 4 phase) were synthesized by an extensive annealing of several hundreds of hours in order to come close to thermodynamic equilibrium. The microstructure reveals an intergrowth of lamellae with different n (n = 1-5, 7) with an average volume fraction of the n = 4 phase of about 15%. The highest T(c) is about 110 K and superconducting phases with T(c) > 110 K are not detectable. However, the distribution of phases with different n is not homogeneous but varies considerably between the bulk and the grain boundaries. Especially the n = 2 phase is preferentially located at the grain boundaries and inhibits a continuous superconducting path for the majority n = 3 phase in the ceramic material. In addition to the intergrowth of lamellae with different n special grain boundaries of pure twist and pure tilt type are encountered; the possible role of grain boundaries for flux pinning is discussed.