Actually, you are wrong.
A work is specifically defined as a "work of righteousness" which a man would use as an earning to buy his way into heaven. Please go to Romans 3 & 4.
Righteousness Through Faith21But now a righteousness from God, apart from law, has been made known, to which the Law and the Prophets testify. 22This righteousness from God comes through faith in Jesus Christ to all who believe. There is no difference, 23for all have sinned and fall short of the glory of God, 24and are justified freely by his grace through the redemption that came by Christ Jesus. 25God presented him as a sacrifice of atonement,[i] through faith in his blood. He did this to demonstrate his justice, because in his forbearance he had left the sins committed beforehand unpunished– 26he did it to demonstrate his justice at the present time, so as to be just and the one who justifies those who have faith in Jesus.
27Where, then, is boasting? It is excluded. On what principle? On that of observing the law? No, but on that of faith. 28For we maintain that a man is justified by faith apart from observing the law. 29Is God the God of Jews only? Is he not the God of Gentiles too? Yes, of Gentiles too, 30since there is only one God, who will justify the circumcised by faith and the uncircumcised through that same faith. 31Do we, then, nullify the law by this faith? Not at all! Rather, we uphold the law.
Romans 4
Abraham Justified by Faith
1What then shall we say that Abraham, our forefather, discovered in this matter? 2If, in fact, Abraham was justified by works, he had something to boast about–but not before God. 3What does the Scripture say? “Abraham believed God, and it was credited to him as righteousness.”[j]
4Now when a man works, his wages are not credited to him as a gift, but as an obligation. 5However, to the man who does not work but trusts God who justifies the wicked, his faith is credited as righteousness. 6David says the same thing when he speaks of the blessedness of the man to whom God credits righteousness apart from works:
7"Blessed are they whose transgressions are forgiven, whose sins are covered. 8Blessed is the man whose sin the Lord will never count against him.”[k]
As you can see from Rom 4:5, faith is not a work. Throughout these verses faith is ALWAYS contrasted with works and law. Always.
Faith and Grace go together as do works and the Law.
To him that worketh not but believeth on him that justifieth the ungodly, his faith is counted as righteousness.