How about this? (works for me with test data)

use strict;
use warnings;

my %code_to_full;
my %field_by_code;

open my $f, '<', 'test.txt'     or die "open: $!";

my $last_code;
while (<$f>) {
    my ($code, $full) = /^([A-Z]{2}):\s+(.+)/i;
    if ($code && $full) {
        $code_to_full{$code} = $full;
        $field_by_code{$code} = '';
        $last_code = $code;
    }
    else {
        unless ($last_code) {
            warn "No code and last_code blank; this shouldn't happen";
        }
        $field_by_code{$last_code} .= $_;
    }
}

for (sort keys %code_to_full) {
    print "Code: $_\n";
    print "Full: $code_to_full{$_}\n";
    print "Field data: $field_by_code{$_}\n\n";
}
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Things I'd like to point out:

• use of strict
• lexical filehandles
• error checking on system call (open)