Two Factor Authentication Code

2 factor authentication always uses a six digit code - Two-factor authentication for Apple ID - Apple Support

The older, 2 step verification system uses 4 digit codes - Two-step verification for Apple ID - Apple Support

If you had 2 step verification but updated to 2 factor authentication at any point, then your AppleID will not receive 4 digit codes any longer.

The codes for either system are not permanent codes - they are issued on demand when needed and expire within a few minutes, so there is never a code to remember. Every time you need a code, either system will generate a new, random one.

If the 6 digit code doesn't work, contact Apple ID Support.

Apple ID Support

Apple ID Support (2) 

Apple Support by e-mail or chat    Work through the screens to get a chat option.  You may need to pick a problem that is slightly different than yours to get a chat option.  

Apple Support using Twitter

Or fill out and submit this form.          The form is for iTunes, but it will get passed to the ID Support section.  

Verification code? Device passcode? More information would help.

Verification code - how to get one and sign in with two-factor authentication

Passcode - If you forgot the passcode for your iPhone, iPad, or iPod touch, or your device is disabled

Try using the first link I posted to see if you can get a code.

You are welcome.