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Barrage says that it can target a unit when below the weapon's minimum range, or at an enemy that would normally be out of LoS.

Night fight says that no unit can be targeted outside of 36" and that a unit gets shrouding if it is between 24" and 36" away from the firer.

When I want to fire a barrage at a unit outside of 36" during night fight, can I? If I can, and there is something granting that unit a cover save (KFF, area terrain, etc.) do I get the benefit of shrouding when I take that save?

Pg 124 wrote:
Picking a Target and Night Fighting
While the Night Fighting rules are in effect, the distance to a target unit becomes very important - the darkness makes it very difficult to acquire distant targets. The shooting unit cannot pick a target more than 36" away - such units are completely hidden in the darkness.

While you cant pick them as the target of your barrage, if there is an enemy unit within range for you to target, you could scatter into a unit outside that 36" distance.

No. You cannot target the unit.