Makes about 8 servings

1 6-ounce container blackberries
1/2 cup sugar
2 cups gin
1 cup fresh lime juice
Club soda

1.5 oz blackberry syrup
2 oz gin
1 oz lime juice
Foaming agent

Puree blackberries and sugar in a blender. Let stand, stirring occasionally, until sugar is dissolved, about 10 minutes. Strain puree through a fine-mesh sieve into a pitcher. Stir gin and lime juice into pitcher.