Share your experience!
In that case I suggest that you perform a software repair using PC Companion. <-- Click this link for detailed instructions on how to do so, as well as how to make a backup of your phone's data.
If this doesn't help either then I'm afraid your phone is in need of service and you should contact your Local support team for information on where you can find an authorised service center and how to proceed if need be.
Glad to hear a software repair solved it. 
The latest available software version can be seen on our website:
http://support.sonymobile.com/global-en/xperiaz2/software/
However, the availability of software updates depends on your country and/or operator.
The software version shown on our website is the latest available one but as it is stated on the website availability depends on country and/or operator. In this case it seems that the software version mentioned on the website has not yet been released in your country or for your operator.
Regarding the Android 6 update for the Xperia Z2 I do currently not have any information on when it is planned to be released.