Preheat the oven to 425 degrees F. Combine the first 4 ingredients in a large bowl. Add the cod and turn to coat.
Line a baking sheet with parchment paper. Brush the paper with the oil. Spread the panko on a plate. Coat the cod in the panko, gently pressing it on to help it adhere, and then set on the baking sheet.
Bake 6 minutes, and then carefully flip each piece over. Bake 6 minutes more, or until just cooked through.
Note: Panko, coarse, Japanese-style breadcrumbs, can be found in the Asian foods aisle. If unavailable, regular breadcrumbs can be substituted.