@Turbotim Hi and welcome to the Win-RAID forum.
Now that you have identified the correct Intel Management Engine version (v11.8) you will need to download the corresponding tools for your specific Intel PCH (or you get the PCH unsupported message in your first post).
Please read this thread:
Intel (Conv.Sec.) Management Engine: Drivers, Firmware and Tools (2-15)
and then download:
CSME System Tools v11
For CSME v11
This package will contain Intel FPT v.11.
FYI it may not be able to read/write to all areas of the BIOS EEPROM due to vendor BIOS locks.
In most cases you can get a full backup.
Also note that the BIOS for some notebook/laptops is split across two separate chips, so if you are planning to edit and re-flash the modded BIOS, you may need to split the BIOS accordingly and flash each EEPROM with a hardware programmer.
Also, there is a separate chip for the Embedded Controller (EC) firmware. Do not accidentally erase/overwrite this chip as it can be very troublesome to find and restore the original EC firmware!