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Have any parts been replaced on the phone by non Apple Service Providers?

If you tried all those things, without getting a different result, contact Apple, to get it checked.

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If you see one of the errors below, you might have a hardware issue:

• 1, 3, 10, 11, 12, 13, 14, 16
• 20, 21, 23, 26, 27, 28, 29, 34, 35, 36, 37, 40, 56
• 1002, 1004, 1011, 1012, 1014, 1667, 1669

Here's what to check. Try again after each step:

1. If iTunes is already open, quit and reopen it.
2. Check your third-party security software.
3. Make sure that your USB cable, computer, and network are reliable. Then try twice more to restore your device.
4. Check for outdated or modified software. 

If you still see the error, contact Apple Support.

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copied from: Get help with iOS update and restore errors - Apple Support

As there is only error 56 mentioned in this article, error 66 might also point into the direction of an hardware error.

Did you already get the phone diagnosed by an Authorized Apple Service Provider?

Getting the hardware of the phone checked, is the only way to find out about this error, especially if it comes up during the restore process.