Preheat the oven to 400 degrees F (200 degrees C).
Blend Spreadables butter with chives, parsley, lemon juice, lemon zest, garlic, and mustard until well combined; set aside.
Lay 4 large sheets of parchment on a work surface. Mound an equal portion of the zucchini, red pepper, and carrot in center of each sheet. Sprinkle evenly with half each salt and pepper.
Top vegetables with a piece of cod. Sprinkle evenly with remaining salt and pepper. Dollop butter mixture evenly over fish and vegetables. Seal packets by bringing up the sides and folding down tightly. Fold under ends tightly. Transfer to a large, rimmed baking sheet.
Bake for 20 minutes. Let rest for 5 minutes; carefully open packets to serve.