Scanning tunneling microscopy/spectroscopy (STM/STS) measurements were carried out on a multi-layered cuprate superconductor Ba$_2$Ca$_5$Cu$_6$O$_{12}$(O$_{1-x}$,F$_x$)$_2$. STM topography revealed random spot structures with the characteristic length $le 0.5$ nm. The conductance spectra dI/dV(V) show the coexistence of smaller gaps $Delta_S$ and large gaps (pseudogaps) $Delta_L$. The pseudogap-related features in the superconducting state were traced with the spatial resolution of $sim$ 0.07 nm. Here, $I$ and $V$ are the tunnel current and bias voltage, respectively. The temperature, $T$, dependence of $Delta_S$ follows the reduced Bardeen-Cooper-Schrieffer (BCS) dependence. The hallmark ratio 2$Delta_{S}(T=0)/k_B T_c$ equals to 4.9, which is smaller than those of other cuprate superconductors. Here, $T_c$ is the superconducting critical temperature and $k_B$ is the Boltzmann constant. The larger gap $Delta_L$ survives in the normal state and even increases with $T$ above $T_c$. The $T$ dependences of the spatial distributions for both relevant gaps ($Delta$ map), as well as for each gap separately ($Delta_S$ and $Delta_L$) were obtained. From the histogram of $Delta$ map, the averaged gap values were found to be $bar Delta_S = sim 24$ meV and $bar Delta_L = sim 79$ meV. The smaller gap $Delta_S$ shows a spatially homogeneous distribution while the larger gap $Delta_L$ is quite inhomogeneous, indicating that rather homogeneous superconductivity coexists with the patchy distributed pseudogap. The spatial variation length $xi_{Delta_L}$ of $Delta_L$ correlates with the scale of the topography spot structures, being approximately 0.4 nm. This value is considerably smaller than the coherence length of this class of superconductors, suggesting that $Delta_L$ is strongly affected by the disorder of the apical O/F.
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