Result (orderd):
a
g
x
ä

##</code><code>##

Right order:
a
ä
g
x

##</code><code>##

$dbh = DBI->connect( "dbi:SQLite:files/database/data.db" ) || die "Cannot connect: $DBI::errstr";

$selected = $dbh->selectall_arrayref("SELECT ID,column1,column2  FROM table order by column1 collate NOCASE");

foreach my $row_db (@$selected ) {
my ($ID, $column1, $column2) = @$row_db;
print "$column1\n";
}