In a medium mixing bowl whisk together the flour, baking powder, baking soda and table salt then set aside.
In the bowl of a stand mixer fitted with a paddle attachment, beat the butter and sugar until light and fluffy, about 3 minutes. Add the eggs, one at a time, beating well after each addition. Beat in the vanilla and the lime juice then alternate adding the flour mixture and the buttermilk, starting and ending with the flour mixture. Stir in the lime zest and shredded coconut.
Prepare a 8”x4” (1½-pound) loaf pan with butter and flour then evenly spread the batter in the pan. Bake until a toothpick or knife inserted into the center comes out clean, about 45 to 50 minutes. Let cool for 10 minutes then remove the bread from the pan.
For the coconut glaze:
In a small mixing bowl whisk together the coconut milk and confectioners’ sugar until smooth. Spoon the glaze over the top of the bread and top with shredded coconut and lime zest.