God's words are the highest authority.
Sin separates us from God, and all have sinned and come short of the glory of God.
God wants people to abstain from sin, but in the Old Testament they could not have the Spirit, so God had them do physical ordinances, and the blood of animals covered their sins until Jesus came, and physical blessings in the Old Testament.
God's word to be obeyed, and important.
In the New Testament people can have the Spirit, which if they hate sin, and do not want sin, by the Spirit they can abstain from sin, and the blood of Jesus completely washes away their sins, giving them a spiritual relationship with God, and they can love people perfect by the Spirit, and love is the fulfilling of the law, and spiritual blessings in the New Testament.
God's word to be obeyed, and accomplishes more among people than the Old Testament, and the ultimate benefit to mankind, and God operating more among people, and His word understood greater, and His authority understood greater.
Who is Jesus, God manifest in the flesh, and is God without a beginning, who gave people this spiritual benefit, and the words of eternal life, the New Testament.
Yes, I would think that Jesus' words would have the highest authority.
Now while all the writers words were given by the Holy Spirit, Jesus words are the highest authority for it is the New Testament, and the end result of what God has planned for the saints eternal life.
Jesus' words are the highest authority for it is the highest benefit, and pleasing to God that the saints are led of the Spirit, than the Old Testament, and while the Gospels wrote of Jesus and are the words God wanted them to write, they do not apply unless the words of Jesus are in effect.
Without Jesus first telling the words and they go in to effect then nothing written about them matters, for eternal life does not go in to effect until Jesus first tells those authoritative words.
The Gospels, the words mean nothing, unless Jesus first gave us those authoritative words.
Jesus gave the words first then they were written down later.
So in that sense Jesus words are the highest authority, for He gave the words first then they were written down, and the highest benefit to mankind, and people can understand the truth of God better by the Spirit than any time before that, but all the words of God are authority, but Jesus' words are the highest authority because it is the highest revelation of God to mankind than in the past, being able to understand God and His word at a spiritual level which transcends any words on a physical level in the Old Testament.
1Co 2:9 But as it is written, Eye hath not seen, nor ear heard, neither have entered into the heart of man, the things which God hath prepared for them that love him.
1Co 2:10 But God hath revealed them unto us by his Spirit: for the Spirit searcheth all things, yea, the deep things of God.
1Co 2:11 For what man knoweth the things of a man, save the spirit of man which is in him? even so the things of God knoweth no man, but the Spirit of God.
1Co 2:12 Now we have received, not the spirit of the world, but the spirit which is of God; that we might know the things that are freely given to us of God.
1Co 2:13 Which things also we speak, not in the words which man's wisdom teacheth, but which the Holy Ghost teacheth; comparing spiritual things with spiritual.
1Co 2:14 But the natural man receiveth not the things of the Spirit of God: for they are foolishness unto him: neither can he know them, because they are spiritually discerned.
1Co 2:15 But he that is spiritual judgeth all things, yet he himself is judged of no man.
1Co 2:16 For who hath known the mind of the Lord, that he may instruct him? But we have the mind of Christ.
The people in the Old Testament could not attain to the truth we can attain to in the New Testament, so I will say Jesus' words are the highest authority.
For what has more authority to have a law, or to enforce that law and it goes in to effect to punish, for the words in the Old Testament were important, but the words in the New Testament are greater for it is spiritual, and it goes in to affect to the highest blessing, although all of God's word is important.