  We report the discovery of a self-doped multi-layer high Tc superconductor
Ba2Ca3Cu4O8F2(F0234) which contains distinctly different superconducting gap
magnitudes along its two Fermi surface(FS) sheets. While formal valence
counting would imply this material to be an undoped insulator, it is a
self-doped superconductor with a Tc of 60K, possessing simultaneously both
electron- and hole-doped FS sheets. Intriguingly, the FS sheet characterized by
the much larger gap is the electron-doped one, which has a shape disfavoring
two electronic features considered to be important for the pairing mechanism:
the van Hove singularity and the antiferromagnetic (Pi/a, Pi/a) scattering.
