This is tested in Joomla 2.5.x only, it may work in J3.x.x

You need to edit the file at root/language/en-GB/en-GB.localise.php and focus on line 64(ish).

Change...

public static function getUpperLimitSearchWord() {
  return 20;
}

to...

public static function getUpperLimitSearchWord() {
  return 100;
}

Remember this can change with subsequent core updates and you will need to change it back. The alternative is an override method.