In a small pot, combine all ingredients and bring to a simmer. Crush the raspberries and basil leaves with a whisk or spoon as you stir the mixture. Continue simmering and stirring until the sugar has completely dissolved.
Allow your syrup to cool completely in the pot, then strain it into a glass or jar.
In a tall glass with ice, combine rum, simple syrup, lime juice, mint and basil leaves, and fresh berries. Top it off with club soda. Stir and enjoy, preferably on a porch!