I've never heard the term HGTE suspension module, exactly what is that? I did lower my car a bit but I stayed on the standard springs since I didn't want to go lower. I will be putting HGTE wheels on for next year's driving season with 255/35-20 and 315/35-20 P zeros which I'm sure will help. I'm also looking at upgrading the ECU.
The HGTE had a different suspension mapping than the GTB. The TCU is mapped differently too. And yes, I have HGTE upgrade (full upgrade was over $42K USD back around 2010). I run those tires as well.
As noted by Skidkid, it is damper mapping for the magnetorheological dampers. A nice video here from fifth gear Obviously the HGTE suspension mapping is designed around the HGTE springs ARB and wheel size but for me, has worked well with the GTO springs and ARB. I also have the HGTE TCU, the gearbox programming is so much better than the standard GTB. Of note, it was supposed to be a 2 hr job for Ferrari to install but took 8 hours as they had difficulty getting the TCU to copy over and save the gearbox / clutch positions.