If you really want to do it with a regex you can:

use strict;
use warnings;
use noname1;

my $str = 'ASBSDEC 34 GADVVEEVEETTE 56 IOEOREAK GKJEOG EFEAF 1090 DAFF
+EE 376';
my $result;
my $biggest = 0;

1 while ($str =~ /(\w+)\s+(\d+)(?{if($2 > $biggest) {$result=[$1, $2];
+ $biggest=$2}})/gx);

print "$result->[0] $result->[1]";
[download]

Prints:

EFEAF 1090
[download]