Not my righteousness, but God’s righteousness
Rom 1:16-17 For I am not ashamed of the gospel of Christ: for it is the power of God unto salvation to every one that believeth; to the Jew first, and also to the Greek. (17) For therein is the righteousness of God revealed from faith to faith: as it is written, The just shall live by faith.
Verse 16 is a well-known verse, but verse 17 contains a very important statement which tells us that within the gospel, God’s righteousness is made manifest.
The righteousness of God without the law has been made known, Rom 3:21. So, this is not a question of your righteousness, it's a question of God's righteous. The gospel tells us that God freely justifies the one who believes in Jesus, because, without this grace of God, there is NOTHING that we can do to save ourselves. If it was up to us, God could not justify us, because we're guilty in his sight!! So, now it's up to God, and the question is, will God justify ungodly men?