A dispensation of the gospel is a period of time in which the Lord has at least one authorized servant on the earth who bears the holy priesthood and the keys, and who has a divine commission to dispense the gospel to the inhabitants of the earth. *
*Dispensations (churchofjesuschrist.org)
Enoch is one of the most enigmatic characters in the Bible. References to him in the Bible are limited:
In Genesis we read:
Jared begat Enoch. . . and Enoch lived sixty-five years and begat Methuselah. And Enoch walked with God ... and begat sons and daughters. And all the days of Enoch were three hundred sixty and five years And Enoch walked with God and he was not: for God took him. (Genesis 5: 18, 21-24)
In the New Testament, Jude tells us that Enoch was the seventh generation from Adam and that he prophesied for the coming of the Messiah, Jesus Christ, who would judge the ungodly. (Jude 1: 14)
In Hebrews we read: By faith Enoch was translated that he should not see death; and was not found because God had translated him: for before his translation he had this testimony, that he pleased God. (Hebrews 11:5)
That is very limited information about this great prophet and head of the dispensation between Adam and Noah. For that, we have to turn to latter-day revelation. The Pearl of Great Price is exactly that - a pearl of great price - for the information it gives us about Enoch. After giving the generations after Adam, in far more detail. Moses tells us that all the righteous descendants from Adam were preachers of righteousness, and spoke and prophesied, and called upon all men everywhere to repent; and faith was taught unto the children of men. (Moses 6: 23)
One day, according to this account, Enoch was out among the people when the Spirit of God descended from heaven and Enoch heard a voice saying: Enoch, my son, prophecy unto this people, and say unto them, Repent. God then tells him the sorry state of the human race and intimates that a judgment is coming against them. Later, Enoch saw the Lord and spoke with Him, face-to-face (Moses 7:4) Then, in one of the most chilling verses in scripture, the Lord tells Enoch that He will destroy the residue of the people because they have become wicked to the degree that any spirits sent to earth through them would have no opportunity to be righteous.
Then Enoch was lifted up . . . and the power of Satan was upon all the face of the earth. . . And he beheld Satan; and he had a great chain in his hand, and it veiled the whole face of the earth with darkness; and he looked up and laughed, and his angels rejoiced. (Moses 7: 24, 26) And Enoch understood.
Then Enoch noticed God weeping and asked how is it that thou canst weep? (Moses 7: 31) The Lord explained that because He knew the fate of these rebellious ones who were, even so, his own children and the workmanship of [His] own hands. . . Wherefore, for this shall the heavens weep . . . (Moses 7: 32, 40)
Then Enoch began to weep. The Lord allowed him to see his great- grandson, Noah, building an ark. And the Lord . . . covenanted with Enoch, and swore unto him with an oath, that he would stay the floods, that he would call upon the children of Noah; And He sent forth an unalterable decree, that a remnant of his (Enoch's)seed should always be found among all nations, while the earth should stand. (Moses 7: 51-52)
This was an unconditional promise to Enoch. We don't speak of the Enoch covenant, but God made him that promise specific to him. Through Noah, Enoch's seed was saved upon the waters.