Macerate the white peach slices in a small saucepan with the sugar and water. Once the peaches have been made relatively pulpy, bring the mixture to a boil over medium heat, then lower the heat to a simmer and allow to cook for 30 minutes.
Remove it from the heat and allow to cool completely before straining the peach pulp out and reserving the syrup. Keep the syrup refrigerated until use.
Muddle 2 of the peach slices in the bottom of the serving glass. Add the gin, club soda, 3 tablespoons of the simple syrup, and the turbinado sugar. Stir until blended. Garnish with the raspberries and float the remaining two peach slices on top of the drink to form a heart. Serve immediately.