How to recover Bitcoin files from 2011 that were erased using the Gutmann method
Any files erased using the Gutmann method cannot be recovered. The Gutmann method is actually overkill on modern disk drives.
At best, if empty space on the drive has not also been overwritten, you might recover fragments of data from previous versions of files or temporary files. If the files have not been used since 2011 this is extremely unlikely. The more use you make of the computer since the deletion, the less likely any recovery.
The best (and probably only) way to recover control over the money is to simply recreate the wallet using backups of the files or from the written copy of the private keys which you presumably made.