Christ is your righteousness. More important than this however is the fact that Christ is your life. This is more important because righteousness is a sub-category of life and love. Righteousness flows out of life and is love. Jesus is all of this in His person.
Life, love and righteousness are properties of persons. They are not properties of things which are inert with no more life than a stone or a cucumber. For this reason we are to live in joy in order to be better than cucumbers. As sons we live in Jesus and not in the law or some system of morality and ethics.
The effect of Christ in you is direct. By His Spirit, He manifests Himself as you. In the spirit, you are the effect, the result and the manifestation of the Son of Man who is fully God. Filled with Him you are spirit and life. You are a son and not a moral robot.
To live from a system of morality and ethics is to short change yourself. This is not primarily what the Kingdom is. The resurrection of Jesus, of which you are a part, lifts you out of abstractions and includes you in a life – positions you in the life of Jesus and by relationship in life of the trinity.
When Christ is your life – and He already is – you are the expression of Him. You are the son of our Father and a supernatural being in-breathed with the presence of Father. The other side of His indwelling presence is you as your real self – you as a son/daughter of God.
You can live in this directness and union or you can live in derivatives and substitutes. If you do the latter you can never fully worship God or realise the potential of yourself as a daughter or a son. In Galatian Paul calls this being the sons of the slave woman. But when Christ Himself is our life the potential of your sonship is infinite. You touch the world with spirit and life because you are spirit and life.