“your righteousness exceed.” This is one of the places where the word “righteousness” does not refer to salvation, but refers to doing right in the sight of God and others. It is obeying God and treating others in a godly and just fashion. The Pharisees were hypocrites and were not doing right by God and others, which is why Jesus called them “snakes” and challenged them with, “How can you escape the judgment of Gehenna” (Matt. 23:33). Here in Matthew 5:20, Jesus boldly stated to the people that unless they obeyed God and treated people in a godly and just manner, and certainly better than the Pharisees did, they would not be granted everlasting life. [For more on this use of “righteousness,” see commentary on Matt. 5:6].
“enter the Kingdom of Heaven.” In this context, the phrase “enter Kingdom of Heaven” means to enter the future kingdom of Jesus Christ when he reigns as king on earth. It means being in the resurrection of the righteous (the first resurrection) and being granted everlasting life.
[For more on Jesus reigning on earth and the names of his future kingdom, see Appendix 3, “Christ’s Future Kingdom on Earth.” For more on the resurrections in the future, see commentary on Acts 24:15].