Canonicalise the data and look for multiples. The grep tests for numbers where there are a number of multiples of which at least one is a pair. This solution works with numbers of any length and can be made to work with triples, quads etc. just by changing the grep test.
The OP didn't make it clear whether a number such as 0101 that has two pairs should be counted. You can always test the number of members of the list returned by the grep.
while (<DATA>){
print "$_" if grep {length $_ == 2} join('', sort split //, $_) =~
+ /((\d)\2+)/g;
}
__DATA__
0000
0001
0002
0003
0004
0005
0006
0007
0008
0009
0010
0011
0012
0013
0014
01511
451411
gives
0011
0012
0013
0014
451411