Allow me to introduce you to GRASP, a software that was written largely by now 92-year-old Ian Grant and now 94-year old (5 days from now) Charlotte Froese Fischer whose PhD supervisor was Douglas Hartree from the Hartree-Fock method; but
the software has been maintained throughout all of these decades and is open source on GitHub with some commits to "GRASP 2018" being pushed within the last year!
GRASP stands for General Relativistic Atomic Structure Program and was originally written in an older version of FORTRAN, but it has been modernized to Fortran 90 and is parallelized using MPI. In addition to the first link that I provided, which is the HTML/doxygen (web-based) version of the documentation, the the PDF version is available here.
If you click on the first link and search QED in the search bar, you'll see a variety of QED functions and other results, which I'll list below:
Also if you search QED in the PDF documentation which I linked earlier in this answer, you'll find that the vacuum polarization and self-energy terms, which are considered the leading QED effects are included in the
rci (relativistic CI) routine:
rci, rci_mpi - perform relativistic configuration interaction (RCI) calculation with transverse photon (Breit) interaction and vacuum polarization and self-energy (QED) corrections.
Although the term QED appears 30 more times in that document, it's all in relation to the RCI routine, and there's a reference from over 40 years ago by Ian Grant himself (and others) in relation to QED corrections for the multi-configurational Dirac-Fock (MCDF) method, which can be considered a relativistic version of MCSCF (see What are the types of MCSCF?):
B.J.McKenzie, I.P.Grant and P.H.Norrington "A program to calculate transverse Breit and QED corrections to energy levels in a MCDF environment" Computer Physics Communications. 21, 233-246 (1980); ibid 23, 222 (1980).