What can you say about The Epic of Gilgamesh just as a story with meaning? Think of the epic outside of historical context and cultural contingencies.
The meaning of The Epic of Gilgamesh as a story lies on two levels. The first level of meaning is participation in the physical world and the second is participation in the metaphysical world. On the first physical level the meaning of the story is divided. On the one hand, Gilgamesh and Enkidu define themselves and find their fulfillment through the physical feats they perform and the victories over obstacles that they gain. On the other hand. Enkidu incurs the wrath of the gods, especially Ishtar, by defeating the evils sent to Earth as punishments. His penalty is death. The implied lesson is that certain opponents should not be challenged and fought; certain supernatural achievements should not be undertaken.
On the second metaphysical level the meaning is also divided. On the one hand, Gilgamesh does not find the goal of his quest: He does not learn the secret to immortality. In a supernatural sense, Enkidu is always with Gilgamesh, a story fact that gives a hint to the nature of immortality available to mortals. On the other hand, Gilgamesh's quest is not unprofitable because, though he fails in realizing his metaphysical goal in the supernatural world (noting that he never failed in his goals in the physical world), he attains that which he had not the wisdom to strive for: He attained wisdom itself and the ability to rule with mercy and justice and goodness.