Jesus said, except your righteousness shall exceed the righteousness of the scribes and Pharisees, ye shall in no case enter into the kingdom of heaven" (
Matthew 5:20)
This is part of what we call "the sermon on the mount." In it He mentioned several "rules/commandments" of God and several deeds of righteousness and acts of charity and devotion which are part of the lives of His followers. But, He emphasized that the "good stuff" His people do comes from a righteousness within and is not something we put on or impose on ourselves.
The Apostle Paul contrasted the two righteousness in
Romans 10:2-4.
When you invite Jesus into your life, He comes in and you receive not only salvation and a new life, you receive the righteousness of Christ and also His holiness and you become righteous and holy enough to enter Heaven.
As the song says, we are "faultless to stand before His throne, dressed in His righteousness alone."