Reconstructed synagogue at Capernaum

Was this the synagogue in which Jesus delivered the epochal sermon? This synagogue is dated to the fourth century on the basis of coins found under the floor.  However, a major earthquake devastated much of the region in 363 A.D.  Is it possible that this synagogue was rebuilt from the same materials used in the synagogue of Jesus' time?   A study of the foundation shows that this structure was built on top of an earlier structure.

129:1.7 Capernaum was a strong Roman military post, and the garrison's commanding officer was a gentile believer in Yahweh, "a devout man," as the Jews were wont to designate such proselytes. This officer belonged to a wealthy Roman family, and he took it upon himself to build a beautiful synagogue in Capernaum, which had been presented to the Jews a short time before Jesus came to live with Zebedee. Jesus conducted the services in this new synagogue more than half the time this year (his twenty-seventh year), and some of the caravan people who chanced to attend remembered him as the carpenter from Nazareth.