To make the salsa, use a vegetable peeler to slice the cucumbers thinly lengthways. Place the slices in a bowl and add the preserved lime, mint and lime juice. Mix it all together and rest a plate on the surface to weigh the ingredients down. Chill in the fridge for 2-3 hours.
Brush the barramundi lightly with olive oil and a squeeze of lime juice. Grill the fish for a couple of minutes each side. Serve with steamed greens and cucumber salsa.