Luke 7:4

And they, when they came to Jesus, besought him earnestly, saying, He is worthy that thou shouldest do this for him; for he loveth our nation, and himself built our synagogue.

Clearly, the centurion had remained at home (Luke 7:6), and the Jewish elders actually bore the request to Jesus.

Our synagogue ... McGarvey wrote that:

The ruins of Capernaum show the ruins of a synagogue. It was a beautiful structure, built of white limestone, shows by its architecture that it was built in the time of the Herods, and there is little doubt that it is the one which this pious Gentile erected, and in which Jesus taught and healed.[8]

Thus, God raised up a devout Gentile to provide a platform from which many of the marvelous teachings of the Lord would be announced (see John 6:59).

How strange it is that this Roman centurion, a Gentile, and an officer in the hated army of the oppressors, should have received such a commendation as the Jewish elders in Capernaum delivered to Jesus on his behalf. He was one of a class of persons who rose above the base morals of the ancient empire and who rejected the vanity and falsehood of the pagan religions.

He was one among the proselytes, whom the providence of God had so wonderfully prepared in all the great cities of the Greek and Roman world as a link of communication between Gentile and Jew, in contact with both - holding to the first by their race, and to the latter by their religion; and who must have materially helped in the early spread of the faith.[9]

[8] J. W. McGarvey, The Fourfold Gospel (Cincinnati, Ohio: Standard Publishing Company, 1914), p. 271.

[9] Richard Trench, Notes on the Miracles of Our Lord (Old Tappan, New Jersey: Fleming H. Revell Company, 1953), p. 241.