I can't write new settings to the S22-register.

On the MT5600ZDX modems the S22 register is a read-only register that holds a variable decimal value that will change based on these AT command settings:

ATL1 sets speaker volume Low
ATM1 sets speaker control off when carrier detected
ATX4 Sends all responses
Hence
ATS22?
117
If you change the AT commands to
ATL3
ATM0
ATX0 then
ATS22? will = 001

Note: You cannot directly edit the S22 Registe. Only the AT command Settings previously mentioned, will change the value.