I wouldn't refer to the CEO's handbook, I quoted it so that you could see that 624 wasn't a random addition.
The wrong contravention code isn't a statutory defence, so tread lightly. I am simply suggesting that you challenge because although the PCN states that 4 wheels were on the footway, and you assume* it is this which gave rise to the PCN, as they will see only one wheel was on the footway. It must surely follow that the CEO was mistaken an the PCN must be cancelled.
They won't, but what you're doing is testing them within the 14-day period.
*- you say you didn't know about the footway prohibition beforehand, so all you're doing is reflecting on their PCN i.e. 4 wheels = penalty, but it wasn't 4 wheels.