Is it possible to grab somebody who is not adjacent?
If your natural melee reach is 1, then No.
GrabDDI explicitly states that you don't have to count the extra reach of a weapon, while a Grasping WeaponDDI doesn't define any exception to this rule.
This is somewhat reinforced by the Grasping Weapon encounter power:
Power (Encounter): Free Action. Use this power when you hit with the weapon. Pull the target 1 square into an unoccupied space adjacent to you. The target is grabbed (until escape).
It first pulls the target within melee reach in order to allow a "regular" grab.
If your melee reach is higher than 1 (Large or larger monster) then you can grab creatures not adjacent to you (so Yes).
Furthermore, with a Large or larger reach weaponDDI, you can target creatures one square beyond your normal melee reach. But still, you cannot initiate a grab at this distance (unless you are using the Grasping Weapon encounter power).