I've noticed that most locations within China do not have admin codes and those which do are not correct.
The link below points to the official admin codes and hierarchy of all districts within China. The page is in Chinese but it's very easy to navigate. Centered on the page are the names of each province, clicking these will list the cities and codes within each. Further clicks will list the distracts and subdistricts of each giving the full Admin4 codes.
All of the names should already be present within the geonames database, but the admin codes and hierarchy needs updating.