Galatians 2:14-16 But when I saw that they were not straightforward about the truth of the gospel, I said to Peter before them all, “If you, being a Jew, live in the manner of Gentiles and not as the Jews, why do you compel Gentiles to live as Jews? We who are Jews by nature, and not sinners of the Gentiles, knowing that a man is not justified by the works of the law but by faith in Jesus Christ, even we have believed in Christ Jesus, that we might be justified by faith in Christ and not by the works of the law; for by the works of the law no flesh shall be justified.But those are all references to the Mosaic Law. It doesn't seem relevant to this discussion of the good works produced by Christian faith.
You’ve stated it very well: works are produced by faith.