A rather simpler and portable version of the above that also contrasts the results with both the sum and product of the same values. It shows how the positional weighting remais true when the sum and product do not:

#! perl -slw
use strict;
use List::Util qw[ sum reduce ];

our $SEED ||=1;

srand( $SEED );

my @data = map{
    [ map{ int rand 4 } 1 .. 6 ]
} 1 .. 20;

my @sorted = map {
    $_->[1]
} sort {
    $b->[0] <=> $a->[0]
} map {
    my $n = reduce{ $a << 2 | $b } 0, @$_;
    [ $n, $_ ]
} @data;

print "@$_\tsum:", sum( @$_ ), "\tproduct: ", reduce{ $a *= $b||1 } 1,
+ @$_ for @sorted;

__END__
P:\test>503446.pl -SEED=-999998
3 2 2 3 1 1     sum:12  product: 36
3 2 0 1 3 2     sum:11  product: 36
3 1 3 1 3 0     sum:11  product: 27
3 1 3 0 0 2     sum:9   product: 18
3 0 2 2 3 2     sum:12  product: 72
3 0 1 1 0 0     sum:5   product: 3
2 2 1 0 1 2     sum:8   product: 8
2 1 1 0 3 2     sum:9   product: 12
2 1 0 3 1 1     sum:8   product: 6
2 0 3 0 2 2     sum:9   product: 24
2 0 1 1 2 1     sum:7   product: 4
1 3 2 2 2 0     sum:10  product: 24
1 3 0 1 3 1     sum:9   product: 9
1 2 1 1 0 1     sum:6   product: 2
1 1 3 2 3 0     sum:10  product: 18
1 0 2 0 1 1     sum:5   product: 2
0 3 3 0 1 2     sum:9   product: 18
0 2 3 2 0 0     sum:7   product: 12
0 2 3 0 3 1     sum:9   product: 18
0 1 3 0 3 1     sum:8   product: 9

P:\test>503446.pl -SEED=1000
3 3 0 3 0 0     sum:9   product: 27
3 3 0 2 3 3     sum:14  product: 162
3 1 3 1 3 0     sum:11  product: 27
3 1 3 0 0 2     sum:9   product: 18
3 0 2 2 3 2     sum:12  product: 72
3 0 1 1 0 0     sum:5   product: 3
2 2 1 0 1 2     sum:8   product: 8
2 1 1 0 3 2     sum:9   product: 12
2 1 0 3 1 1     sum:8   product: 6
2 0 3 0 2 2     sum:9   product: 24
2 0 1 1 2 1     sum:7   product: 4
1 3 2 2 2 0     sum:10  product: 24
1 3 0 1 3 1     sum:9   product: 9
1 2 1 1 0 1     sum:6   product: 2
1 1 3 2 3 0     sum:10  product: 18
1 0 2 0 1 1     sum:5   product: 2
0 3 3 0 1 2     sum:9   product: 18
0 2 3 2 0 0     sum:7   product: 12
0 2 3 0 3 1     sum:9   product: 18
0 1 3 0 3 1     sum:8   product: 9
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