There's a functional module somewhere with reduce in it, I think.

Anyway, you said map, here's my solution...

my @ans = 
    grep {$_}
map {
    my $func = $_; 
    reduce( sub{
    my($first, $second) = @_;
    return ($first eq $second) && $first;
    }
        , map(&$func, @data));
}
map {
    my $ctr = $_; 
    sub
    {
    my $str = $_;
    substr($str, 0, $ctr);
    }
}
(1..length($data[0]));

print pop(@ans), "\n";
[download]

I faked a reduce to test it, it works on this dataset.