The correct guns are the LVL 115 16" TD-18 triples. These are the best guns by far, and you'll be able to fit 4 binds. The only serious alternative would be the LVL 115 16" AC-13 quads (also 4 binds). However, these guns have reduced shell damage, so they actually tend not to hit as hard as the triples, leaving no benefit and several drawbacks.
The 115 guns cheat a little in that their ammunition uses only a fraction of the space as that on normal guns, and as a result, they can fit twice as many binds even with a higher space requirement for the turrets.