Permutapalindromic numbers
05AB1E, 15 14 13 bytes
Saved a byte thanks to Emigna! Code:
µNœvyJÂïÊP}_½

Explanation:
µ               # c = 0, when c is equal to the input, print N.
 N              # Push N, the iteration variable.
  œ             # Push all permutations of N.
   vyJ    }     # For each permutation...
      Â         #   Bifurcate, which is short for duplicate and reverse.
       ï        #   Convert the seconds one to int, removing leading zeros.
        Q       #   Check if they are not equal.
         P      #   Product of the stack.
           _    # Logical not.
            ½   # Pop a value, if 1 then increase c by 1.

Uses the CP-1252 encoding. Try it online!.