Unlock iPhone 5s (previous carrier: AT&T)

I bought iPhone 5s with the AT&T Next plan on october 3rd, 2013, and accelerated the payments. I moved to Europe in December, and was told that all I had to do was to contact AT&T and ask for a device unlock code. When they had done their part, all I had to do was to connect to iTunes, take a backup of my phone and then restore from backup. I did all of this, and inserted my European SIM card.

The message I get is:

"SIM not valid"

"The SIM card that you currently have installed in this iPhone is from a carrier that is not supported under the activation server. This is not a hardware issue with the iPhone. Please insert another SIM card from a supported carrier or request that this iPhone be unlocked by your carrier. Please contact Apple for more information."

As mentioned earlier, I already have contacted my carrier and they unlocked the phone. What can I do to unlock this phone?

Thank you