You dreaming, not one scripture says that Faith is not a work of the Law, because it would be in contradiction Jesus words here Matt 23:23 !
Jesus doesn't come right out and say that it is a work of the law there.
It is an intangible--an attribute of God, a characteristic that all of God's people should have. That stands in opposition to the externals of the law which they were obeying. I
It is a "heart" matter.
Jesus taught the same thing about adultery:
Matthew 5:27 Ye have heard that it was said, Thou shalt not commit adultery:
28 but I say unto you, that every one that looketh on a woman to lust after her hath committed adultery with her already in his heart.
They no doubt obeyed the former--the external part of the law.
But it was the inner heart that mattered. "Just to look upon a woman with lust" was also adultery.
This is the same principle that Jesus was teaching in Matthew 23.
It is the heart attitude that counts.