Line 120 of your data file contains a record where the key field (characters 4 through 7) are not one of "TTGT" "GGTT" "ACCT"

To handle that, try this modified version:

#! perl -sw
use strict;

my %outFHs = map {
   open my $fh, '>', "$_.fastQ" or die $!;
   $_ => $fh;
} qw[ TTGT GGTT ACCT other ];

until( eof() ) {
    my @lines = map scalar <>, 1 .. 4;
    my $barcode = substr $lines[1], 0, 9;
    my $tag = substr $barcode, 3, 4;

    print { $outFHs{ $tag } // $outFGs{ other } } @lines;
}
__END__
usage:
thisScript theBigfile.fastQ

## outputs to TTGT.fastQ GGTT.fastQ ACCT.fastQ
## Unrecognised records are put into "other.fastQ"
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