Put the mint, cucumber, blackberries, lime juice, and sugar in a bowl. With the back of a large wooden spoon, press to bruise everything and to let the juices flow. Pour in the gin and place the bowl in a cool spot to let the flavors marry.
Strain into a pitcher, pressing as much juice out as possible; discard the solids. Divide the marinated gin among four glasses, add ice, and top up with sparkling water. Garnish festively.
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