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Here is where I learn a way to recover iCloud security code:
Actually, there are three ways to recover lost contacts of iPhone, one is from the iTunes backup files, another one is recover them directly from the iPhone with the help of iPhone Data Recovery software, the last one is to restore contacts from iCloud, since you are wondering about the way without the using of iTunes backup, you can choose a kind of iPhone Data Recovery software to recover your contacts in a few steps and it is very easy and fast, you can have a try!
Read more here: http://www.recovery-ipad.com/restore-contacts-from-icloud.html
I mention a link https://discussions.apple.com/thread/5519615?tstart=0, which help you lot to solve the problem.
I’m afraid that you can’t recover it if you entered it too many times. You will likely need to contact Apple Support to regain access.
From Apple Support: "If you enter your iCloud Security Code incorrectly too many times, you won't be able to use that iCloud Keychain. You can contact Apple Support, who can help verify your identity so that you can try again to enter your iCloud Security Code. After a number of incorrect attempts, your iCloud Keychain is removed from Apple's servers and you will need to set up iCloud Keychain again."