use strict;

my @AoA = (
           [ "X", "Z", "W", "X", "Z", "Z" ],
           [ "Z", "Z", "X", "X", "X", "W" ],
           [ "X", "Z", "X", "W", "W", "W" ],
           [ "Z", "X", "W", "X", "Z", "Z" ],
           [ "Z", "X", "W", "X", "X", "W" ],
           [ "Z", "X", "X", "X", "Z", "W" ],
    );
my @col;

for my $row (@AoA){
   $col[$_]{$row->[$_]}++ for 0..$#{$row};
}
for my $v(@col){
  my ($first,$second)= sort {$v->{$b} <=> $v->{$a}} keys %$v    ;
  print ($v->{$first} eq $v->{$second} ? "A":$first, " ");
}
print "\n";
[download]

Prints:
Z A A X Z W

Update: Not sure what you meant by the 60% - perhaps this print replacement :

   print ($v->{$first} == $v->{$second} || 
                $v->{$first} < 0.6 * scalar(keys %$v) 
            ? "A": $first, " ");
[download]