More than the law of Moses
Matthew 5:20
For I say unto you, that except your righteousness shall exceed the righteousness of the scribes and Pharisees, ye shall in no case enter into the kingdom of heaven.
The scribes and the Pharisees were fully engaged in following every aspect of the law. They held themselves to a high standard and persecuted those who did not do likewise. They had a long list of rules to follow, and lines to stay within, and many things they were not allowed to do. In different ways they held others to all of those same standards.
Their way was all about DOING good.
What Christ presented in the sermon on the mount (and in other places later in his ministry and life) is that we must do much more than just follow that law. He gave us a much higher law. A law that is written on our hearts. We must love God with all our might mind and strength, and we must love our neighbor. Truly loving our neighbor is more than just following a checklist of laws. Things that include the complexity different people are not as black and white as a checklist. Serving others, being peacemakers, loving your enemies, having the inner strength to forgive those that hurt you, all lead to back to him. He asks us to follow his example.
His way is all about BEING good.