You have to downgrade to .534, Root with Bin4ry, Install DualRecovery, Backup TA, Update to .136 with the instruction by NUT and pre-rooted .136. Then follow the instruction to Unlock Bootloader. You have to have Unlocked Bootloader to install CM11. Do not flash it on Locked one because you will brick your phone. Also after Unlock Bootloader you Warranty will be void. Read very carefully before attempt anything.
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My Evolution: Sony Xperia Z1 - UB + 4.3 Rooted + Deodexed, HTC HD2, HTC Diamond 2, HTC HD Blackstone, Nokia 7070 Prism, Qtek 9100, Nokia 3100, Motorola T720i, Nokia 3310, Sony Ericson PF 768 (Blue)
How Get Root on Sony Xperia Z1 with Locked Bootloader and the Latest Android 4.4