We report the elaboration of a lyotropic hexagonal mesophase with a very large lattice parameter. The quaternary system studied displays a hexagonal phase of direct type, namely, nonpolar tubes in a polar medium : by varying the ionic force of the polar medium, i.e., by addition of salt, we show that it is possible to realize hexagonal mesophases with swollen cylinders of monitored radius up to 17 nm. Moreover, from microscopic observations we have access to the elastic characteristics of the swollen lyotropic hexagonal phases, quantified by a penetration length lambda. We find that lambda increases with the swelling ratio and interpret this result via microscopic models.