I pulled the patched radio.img from my phone after updating from 4.0.2 to 4.0.4IMM76K. This file should work coming from any radio as it includes the full radio.img, not just the radio.img.p that is in the update from google. I do seem to get a 4G signal where I previously only got a 3G signal (ie in my basement). The .zip includes radio.img, radio-cdma.img, and bootloader.img.
It must be flashed through a custom recovery, fastboot will not work
for the LTE radio.
It flashed fine on my phone, but I'm not responsible for any problems you may have :P.
Thanks to SpringRush
for posting the google link to the update and krazie1
for the logcats that got the filename and probably helped find said link.