Looking on HP's site I see that there's actually a newer Firmware version available (22.214.171.12402). Please download and try updating to this version. Do you see the same error with this version as well?
Intel Customer Support
thanks for the link.
I have just tried it and it came back with the following error
Cannot retrieve current FW Version
This program cannot be run on the current platform
Please confirm that you are running the correct softPaq on its supported platform
I have confirmed that it is a Z440 running Windows 7 32bit and I get the same result on a 64bit workstation.
The behavior sounds like there might be an issue with the MEI driver that's installed. I would suggest downloading and installing the latest version available. After installing the latest version of the driver, reboot and try the firmware update again. If you're still not able to update the firmware, then I would verify with HP that this is indeed the correct firmware update for the Z440 workstation.
MEI 126.96.36.1993: https://support.hp.com/us-en/drivers/selfservice/swdetails/hp-z440-workstation/6978828/swItemId/wk-196750-1