Preheat your outdoor grill to medium-high heat, aiming for a temperature of approximately 400°F (204°C). While the grill warms up, cut four large squares of heavy-duty aluminum foil (about 12×12 inches each) and lay them out on your workspace.
In a small mixing bowl, combine the olive oil, freshly squeezed lemon juice, minced garlic, chopped parsley, dill, salt, pepper, and paprika. Whisk these ingredients together until the oil and lemon juice are well emulsified.
Place one cod fillet in the center of each piece of foil. Divide the sliced zucchini and halved cherry tomatoes evenly among the four packets, arranging them neatly around the sides of the fish fillets.
Drizzle the prepared lemon herb mixture evenly over each piece of cod and the surrounding vegetables. Top each fillet with one or two lemon slices for extra zest. Fold the sides of the foil over the contents and crimp the edges tightly to create a sealed packet, leaving a little room inside for steam to circulate.
Place the foil packets directly onto the grill grates. Close the lid and cook for 12 to 15 minutes. The fish is done when it becomes opaque and flakes easily with a fork. Carefully open the packets—watch out for the hot steam—and serve the fish and vegetables immediately.