Disclaimer: I have an Axis and not an AX40 so I don't know if they have different bridge types.
Is your bridge floating or resting on the body? If it's floating you can lower the 2 bridge posts with a 4mm allen wrench. If it's already resting on the body then my advice will differ from the official EBMM advice.
I am new to the Floyd world, but in my experience the truss rod should primarily be used to control the relief of the neck, not the action. Yes, adjusting the relief does also change the action, but really the truss rod should be used to control the bow of the neck between the first and last frets. If the rod is too tight there will be back-bow and you'll most likely get buzzing. When setting up a guitar I always set the relief first and THEN adjust the action.
Here is the part where I'm a n00b: on the Axis, if the bridge is already flush on the body, you can't lower it any further, but you could shim the neck to lower the action. On the other hand, if you wanted higher action, you could shim the individual saddles with aluminum or copper tape.
Someone more experienced may chime in and scold me for going against official EBMM advice
okey, thats what I thought, i tried lowering adjusting the bridge posts but they where already to tight. yes the bridge is already resting on the body. I have no experience with shims so I wont do that on my own