In a bowl, beat eggs, buttermilk, and butter to blend. In another bowl, mix flour, cornmeal, masa, sugar, baking powder, and salt.
Stir flour mixture into egg mixture just until evenly moistened. Gently stir in berries. Spread level in a buttered 8-inch square pan.
Bake in a 375° oven until a wooden skewer inserted into the center comes out clean, 20 to 25 minutes. Let cool 10 minutes, then cut into 9 squares.
Nutritional analysis per piece.