Christ is righteous. He obeyed the law perfectly and never sinned.
No other human is righteous on their own, as “all have sinned and fall short of the glory of God”, and, “our righteousness is but filthy menstrual rags.”
Humans cannot obtain self-righteousness through following the law, because all humans except Christ have broken the law.
However, we have available to us a righteousness apart from the law – a righteousness that is by faith in Christ.
When we believe the gospel, Christ’s righteousness is imputed to us, thus we have a righteousness that is not from following the law, but rather through faith in Christ.