Are you sure that's 4 grams of carb per serving? My sugar-free vanilla pudding mix (4 serving package) lists 6 grams of carb per serving and that's just for the mix. It's 12 grams per serving made with milk. If you add 2 cups of heavy cream, that's another 13 grams of carb.
What I come up with for a 4 serving package of sugar free vanilla pudding made with heavy cream is 24 grams of carb for the mix and 13 grams of carb for the cream for a total of 37 grams of carb. Divide that by 4 and you get 9.25 grams per serving. Divide by 6 and you still get over 6 grams per serving.
There is a way to cut the carbs further and that would be to use half cream and half water. That would drop the total carb count to 30.5, or 7.6 grams for 4 servings/5 grams for 6 servings.