@array2 =~ /$code/; will give you a warning. Did you read the warning message? You cannot test an RE against an array like that.
grep is sometimes useful for that, but in your case you need another solution, of which there are many.

Here is mine:

#!/usr/bin/perl
use strict;        # Always use strict
use warnings;

# Always test the return value from open
open(my $fh1,"file1.txt") or die "Unable to open file1:$!";
my @array1=<$fh1>;
close($fh1);
chomp @array1;

# Create a hash using the code values from file1
my %hash;
@hash{@array1} = undef;

# Create an RE pattern from code values from file1
my $pattern = join ('|', @array1);

open(my $fh2,"file2.txt") or die "Unable to open file2:$!";;

# If we find the code, increment the count in the hash
for my $line (<$fh2>)
{
    chomp $line;
    if ($line =~ /($pattern)/) {
        $hash{$1}++;
    }        
}
close($fh2);

# Print out the hash
for my $code (keys %hash) {
    print "$code $hash{$code}\n"
}
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