Using a nylon tipped muddler, muddle three lime wedges in bottom of a cocktail shaker until they release their juices. Add cucumber, strawberries and mint and muddle again. The goal is to break up the mint into little pieces that will float in the finished cocktail.
Add ice, gin, simple sugar and thoroughly shake vigorously until the outside of the shaker is frosted and condensed. Taste and adjust simple sugar as needed.
Strain cocktail into a chilled martini glass and garnish rim with a strawberry, a lime wheel, a cucumber wheel and a sprig of mint.