Here is the tutorial to root your Sony Xperia Z1 running Android Lollipop 5.1.1 Build 14.6.A.0.368.
This tutorial is only for Build 14.6.A.0.368 , will work on all models of Xperia Z1 i.e C6902, C6903, C6909, C6943 :)
Disclaimer : I am not responsible if you brick your phone or if u make any other damage to your phone
So Lets Start :
1. First make sure you are running Lollipop 5.1.1 Build 14.6.A.0.368. Go to Settings > About to verify this. The below screenshot is of C6902 but the method will work on all models of Z1 running Build 14.6.A.0.368.
3. Open the KingRoot app from your mobile , Click on "Start Root" , the Rooting Process will start. ( You need to be connected to internet via WiFi or Mobile data )
4. You will see a message saying "Successfully obtain root" when the process is finished.