Preheat the oven to 350 and prepare a loaf pan with parchment and grease. Set to the side.
Chop the strawberries and rhubarb into small pieces. Try to keep them in a similar size.
In a large mixing bowl, whisk together the eggs and the sugars. Whisk until fluffy.
Add in the oil, lemon zest, buttermilk, vanilla, and salt. Mix to combine. Then, add in the baking powder and baking soda.
Using a rubber spatula, fold in the flour. Mix until the batter is streak-free. Then, fold in the strawberries and the rhubarb.
Pour the batter into the prepared cake pan. Bake the cake in the oven for 45-55 minutes, or until a toothpick comes out clean from the pan. Let the cake cool completely on a cooling rack before removing from the pan.