This is stock CAP 2203 (the latest bios) for ASUS P8Z77-M (non-Pro). I added the latest available NVMe mod module: NvmExpressDxe_5.ffs (dated 09/20/2021)
This is for USB Flashback only, it will not work with EZ Flash.
Bios is already renamed as needed for flashing: P8Z77M.CAP
You will need to put this file on USB drive (USB2.0 and the smallest drive possible), formated MBR/FAT32. Don’t use drives that were ever partitioned with multiple partitions in the past.
Instructions: Connect PC to UPS if one is available. Insert the USB drive in the green marked USB slot (check manual if unsure), don’t turn the power on, just press the Bios Flashback for 3 seconds. If everything is OK, Bios Flashback LED will blink for about minute or three. Don’t interrupt the flashing, if blinking starts just wait for at least 5 minutes.
If flashing doesn’t start, try different USB drives, try several if needed. Use USB2.0 and the smallest drive possible, also go for a drive that has never been partitioned with multiple partitions. Don’t ask me why, it just is. I tried many USB drives until I found one that worked for me (my wife’s document USB). 
So to conclude, I used this very same file for my ASUS P8Z77-M and flashed it with Asus Bios Flashback feature. It works. But use with caution, and read up the official guides.
Big thanks to Fernando and Meatwar, and everybody else that contributed.
Also> It is advisable having the standard Asus bios 2203 handy on another PC (or USB drive) just in case something goes wrong and you need to get PC up and working.
Original bios is still available here:
https://www.asus.com/us/supportonly/p8z77m/helpdesk_bios/
More info and guidance//flashing/OS install here:
After flashing, you might need this:
Good luck and best regards,
Van
P8Z77M.zip (4.2 MB)