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Did you post your answer before or after the other answer?
If before, then yes, and the badge awarding system is probably just taking it's sweet time.
If after, then no. Sorry, Enlightened is a tough one.
I believe deleted answers still count for "firstness", so if someone replied before you did, but then deleted their answer, you won't ever see the Enlightened badge. Some moderator/10k+ user will have to confirm for you whether there is a deleted answer on this question.