In Noah's day, the whole world was found to be wicked at such an extreme level that God decided to destroy everything. However, it was Noah who was found to be a righteous man, blameless among the people of his day.
The Lord saw that the wickedness of man was great in the earth, and that every intention of the thoughts of his heart was only evil continually. 6 And the Lord regretted that he had made man on the earth, and it grieved him to his heart. 7 So the Lord said, “I will blot out man whom I have created from the face of the land, man and animals and creeping things and birds of the heavens, for I am sorry that I have made them.” But Noah found favor in the eyes of the Lord.
9 These are the generations of Noah. Noah was a righteous man, blameless in his generation. Noah walked with God. Genesis 6:5-9 ESV
Noah's grandfather was Methuselah, whose name means "his death shall bring judgment". According to the time of his death, he died the year of the flood--supposedly not from drowning but from natural causes. His death brought judgment.
Noah's great grandfather--and Methuselah's father--was Enoch, who is noted as having "walked with God". His walk with God was apparently so close that God took Him straight to heaven.
When Enoch had lived 65 years, he fathered Methuselah. 22 Enoch walked with God after he fathered Methuselah 300 years and had other sons and daughters. 23 Thus all the days of Enoch were 365 years. 24 Enoch walked with God, and he was not, for God took him. Genesis 5:21-24 ESV
So, we know that Enoch was a very righteous man. We also know that Noah was a very righteous man. Thus, it seems that this was a righteous lineage, where the righteous fathers passed on to their children a deep reverence for God.
The evidence is not overwhelming, to be sure. In fact, it's largely circumstantial. Still, the conclusion is reasonable.