I chose to generalize rather than optimize, and I think it lead to an improved solution.

Note that by reversing the lines, we can reuse the left-to-right algorithm to get the right-to-left diagonals. By also reversing the returned list, the line numbers are also made correct.

I first coded this to look for a complete diagonal of all 1 or 2, until I read the "~ 500x50" comment.

#!perl
use strict;
use warnings;

while (<DATA>) {
    chomp;
    my @lines = map { [ split '' ] } split ' ';

    my @diags_LR =         extract_diagonals(        @lines);
    my @diags_RL = reverse extract_diagonals(reverse @lines);
#print "@diags_LR\n@diags_RL\n";

    my @nums = map  { $_ + 1 }
               grep { wanted($diags_LR[$_]) or wanted($diags_RL[$_]) }
               0 .. $#diags_LR;
    print "Diags found in lines: @nums\n  data:$_\n" if @nums;

}

sub wanted {
    my ($diag) = @_;
#    return $diag =~ m{ \A ([12]) \1+ \z }msx; # All 1's or all 2's
    return $diag =~ m{ 1111 | 2222 }msx; # Four 1's or 2's anywhere
}

sub extract_diagonals {
    my @lines = @_;

    my $row_count    = scalar   @lines;
    my $column_count = scalar @{$lines[0]};
    die unless $column_count > 1 and $row_count > 1;
    
    my $diag_length = ($row_count < $column_count) ? $row_count
                                                   : $column_count;

    my @diagonals;
    for     my $c ( 0 .. ($column_count - $diag_length) ) {
        for my $r ( 0 .. ($row_count    - $diag_length) ) {
            my @diag_chars = map { $lines[$r+$_][$c+$_] }
                             0 .. ($diag_length-1);

            push @diagonals, join( '', @diag_chars );
        }
    }
    return @diagonals;
}

__DATA__
ABCDEFGH IJKLMNOP QRSTUVWX
ABCDEF GHIJKL MNOPQR STUVWX
ABC DEF GHI JKL MNO PQR STU VWX
ABCD EFGH IJKL MNOP QRST UVWX
ABCDE FGHIJ KLMNO PQRST UVWXY
220021 000200 020222 020222
100000 010000 001000 000100
102000 010200 001020 000102
102000 010200 001020 000201
[download]

Output:

Diags found in lines: 1
  data:100000 010000 001000 000100
Diags found in lines: 1 3
  data:102000 010200 001020 000102
[download]