and be found in him, not having a righteousness of my own that comes from the law, but that which comes through faith in Christ, the righteousness from God that depends on faith— (ESV)
There is something about everyone of us that wants to be right with God. Oh, I know, there are people who claim to be atheists. They angrily demand that there is no God and that they can prove it. Yet, the reality is God's existence is revealed to all mankind by His Creation. The world around us proves to everyone, even so-called atheists that God exists.
The nagging reality of God's existence leads us to desire to be right with that God. If we ignore God's existence we will miserable because we know we are not right. So, what does mankind do? We try to be good enough for this "God" who must exist. In every generation of mankind we find archaeological evidence of man worshiping some kind of God.
Paul was a man who spent his whole life pursuing God. He achieved levels of self-righteousness that was head and shoulders above everyone else. He was a Pharisee of Pharisees. You could not get any higher in man generated righteousness. Yet Paul says here in this verse that he wants nothing to do with a righteousness of his own. He only wants the righteousness that comes from God.
Paul's admission would be staggering to Jewish readers who knew Paul's background. He was a hero to people who were striving to keep the Law. Paul knew that living a life of only outward morality was a farce. He wanted to be pure on the inside. He knew that the only way to be made right with God is by placing his faith in Jesus Christ who gave his life for mankind.
Are you trying to be good enough? It's time to give up. All of your efforts at righteousness will only make you a nice looking hypocrite. Accept God's free gift. Know Christ. Be found in him alone.