Unfortunately, you have your month and day fields transposed as the third date in the list shows that the format is MMDDYYYY, there not being a month 20 in the year!

If there are many directories to sort there might be some benefit in using a more advanced sorting approach rather than repeatedly substr'inging the same fields as each date is compared with others in turn. I have used unpack as an alternative to substr in the following code. A Schwartzian transform:-

$ perl -Mstrict -Mwarnings -E '
my @dates = qw{
   12112014
   01052015
   02202015
   03102015
   01012011
   04092015
   09092015
   };

say for
   map  { $_->[ 0 ] }
   sort { $a->[ 3 ] <=> $b->[ 3 ]
          ||                                                
          $a->[ 1 ] <=> $b->[ 1 ]
          ||
          $a->[ 2 ] <=> $b->[ 2 ]
        }
   map  { [ $_, unpack q{a2a2a4}, $_ ] }
   @dates;'
01012011
12112014
01052015
02202015
03102015
04092015
09092015
$
[download]

Guttman Rosler transform:-

$ perl -Mstrict -Mwarnings -E '
my @dates = qw{
   12112014
   01052015
   02202015
   03102015
   01012011
   04092015
   09092015
   };

say for
   map { substr $_, 8 }
   sort                          
   map { join q{}, ( unpack q{a2a2a4}, $_ )[ 2, 0, 1 ], $_ }
   @dates;'
01012011
12112014
01052015
02202015
03102015
04092015
09092015
$
[download]

I hope this is of interest.