I think the wider context makes it clear that this refers to the follower of Christ and not Christ Himself
The NKJV translation is:
11 And He Himself gave some to be apostles, some prophets, some evangelists, and some pastors and teachers,
12 for the equipping of the saints for the work of ministry, for the edifying of the body of Christ,
13 till we all come to the unity of the faith and of the knowledge of the Son of God, to a perfect man, to the measure of the stature of the fullness of Christ;
14 that we should no longer be children, tossed to and fro and carried about with every wind of doctrine ...
The word that the NKJV translates as equipping in v.12 is καταρτισμός, which appears only here and, like many words Paul uses, nowhere else in the New Testament nor the Septuagint. The root of the word is αρτιζω, which means to bring to an end, or finish. The prefix κατα- signifies further completeness. "Equipping" probably doesn't capture the whole meaning here. The KJV "perfecting" is probably closer to the meaning. ("Perfecting" is also the word that appears in Orthodox Christian translations - e.g. Eastern Orthodox Bible: New Testament, Orthodox New Testament).
"Edifying" is probably also not the best choice for οἰκοδομή in v.12, which is rooted in the Greek word for the noun "house" (οἰκία or οἶκος). "Edifying" is etymologically correct - rooted in the Latin aedificium, meaning "building" - but building up might be a better word choice.
The Orthodox New Testament, which is fairly literal, translates this passage:
11 And He gave some to be apostles, and some prophets, and some evangelists, and some shepherds and teachers,
12 for the perfecting of the saints, to the work of ministering, to the building up of the body of Christ,
13 until we all might come to the unity of the faith, and of the full knowledge of the Son of God, to a perfect man, to the measure of the stature of the fullness of Christ;
14 in order that we may no longer be infants, tossed to and fro by waves, and carried about with every wind of teaching ...
A Greek commentator, Theophylact, explains the passage as follows:
Till we all attain to the unity of the faith, and of the knowledge of the Son of God
"How long," the Apostle asks, "must those who have received gifts toil and labor to build up the body of Christ? Until we all have attained to the unity of the faith." This means, until we have all accepted one and the same faith, without variations in dogmas and without any schisms between us. Then there will be the true unity of the faith; and then we will know the Son of God - when we are orthodox in our doctrines and when we preserve the bond of love. For Christ is love.
Unto a perfect man, unto the measure of the maturity of the fullness of Christ.
By a perfect man and the measure of maturity, Paul means the perfect knowledge of the dogmas of faith. By the fullness of Christ, he means the full and complete knowledge and faith in Him.