In this paper, we introduce a random environment for the exclusion process in
Zd obtained by assigning a maximal occupancy to each site. This maximal
occupancy is allowed to randomly vary among sites, and partial exclusion
occurs. Under the assumption of ergodicity under translation and uniform
ellipticity of the environment, we derive a quenched hydrodynamic limit in path
space by strengthening the mild solution approach initiated in
\cite{nagy_symmetric_2002} and \cite{faggionato_bulk_2007}. To this purpose, we
prove, employing the technology developed for the random conductance model, a
homogenization result in the form of an arbitrary starting point quenched
invariance principle for a single particle in the same environment, which is a
result of independent interest. The self-duality property of the partial
exclusion process allows us to transfer this homogenization result to the
particle system and, then, apply the tightness criterion in
\cite{redig_symmetric_2018}