Updating old 2 prong outlets to GFCI

I recently purchased an older home in New Jersey and am trying to pass a certificate of occupancy inspection. Part of the requirements is to update all outlets in bathrooms/kitchen/basement to GFCI. However, there is no ground wire in any of the panels so my GFCI electric test still reads "open ground" and the outlet doesn't trip when I hit the "test" button. However, the "test" and "reset" buttons on the GFCI receptacle themselves are working properly and I put the blue sticker on the face plates that says that the system is ungrounded.

Does anyone know if this is up to code or if I will have to pay an electrician to run ground wiring throughout my system for me to all of these outlets?