You don't need a date function to determine the oldest date. Your dates are formatted so that string comparison works. Here is a way to extract the oldest entry for each group:

use List::Util qw( maxstr);

my %tb;
while ( <DATA> ) {
    my ( undef, $group, $entry_date) = split;
    $tb{ $group}->{ $entry_date} = $_;
}

print $_->{ maxstr keys %$_} for values %tb;

__DATA__
34     gr1    2003-03-02
12     gr1    1990-03-14
39     gr3    2002-04-11
66     gr4    2006-03-16
32     gr3    1998-02-13
90     gr1    2004-06-15
55     gr4    1999-06-15
[download]

Update: Code cleaned up

Anno