The Scripture says "the Law is weakened through the flesh"--because it relies on the sinful flesh to perform good deeds, it is a "weak" method of righteousness.Yes. It's the fruit of the Spirit you are describing and the fruit of the Spirit is not bound to Mosaic law because it fulfills the law.
The fruit of the Spirit is: love, joy, peace, long-suffering, kindness, goodness, faith, meekness, self-control; against such things there is no law. (Galatians 5:23).
"Owe no one anything, except to love one another; for he who loves another has fulfilled the law. For: "Do not commit adultery; do not murder; do not steal; do not bear false witness; do not lust;" and if there is any other commandment, it is summed up in this word, "You shall love your neighbor as yourself." Love works no ill to its neighbor, therefore love is the fulfilling of the law." (Romans 13:8-10).
Gal 3:3 also, referring to the works of the Law, describes it as "flesh".
The question as to how these things are is another discussion, but this is what Scripture says.
The "works" that don't justify are good deeds produced by sinful flesh--that has nothing to do with "God's righteousness revealed from faith to faith", which, if not performed, results in "condemnation" (Ro 14:23).