To clean up the code of your first script a little bit, we get this:

#!/usr/bin/perl

use strict; 
use warnings;

use List::Permutor;

my $outfile = 'permutations.txt';
open my $fh, '>', $outfile or die "$outfile: $!";

my $word = 'aabc';
my $perm = new List::Permutor split(//,$word);

while (my @set = $perm->next) {
    my $str = join '', @set;
    print $fh "$str\n";
}

close $fh;
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And if we want to include a modified version of toolic's uniqueness check, we end up with this:

my %seen;
while (my @set = $perm->next) {
    my $str = join '', @set;
    print $fh "$str\n" if ! $seen{$str}++;
}
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