Pat the cod fillets completely dry with a paper towel.
In a bowl, whisk together 3 tablespoons of olive oil, lemon zest, half of the lemon juice, minced garlic, chopped rosemary, parsley, dill, half of the salt, and half of the black pepper.
Coat the cod fillets in the marinade and let them sit at room temperature for 15 to 20 minutes.
Preheat your grill to medium-high heat (375-400 degrees F). Carefully oil the grill grates to prevent sticking.
Grill the cod fillets for 4 to 5 minutes per side. The fish is done when it is entirely opaque, flakes easily with a fork, and reaches an internal temperature of 145 degrees F.
While the fish rests, combine the baby arugula, halved cherry tomatoes, and sliced bell peppers in a large bowl. Toss with the remaining 1 tablespoon of olive oil, remaining lemon juice, salt, and black pepper.
Serve the warm grilled cod fillets immediately alongside the fresh side salad.