I've definitely heard statements from Reformed people denying any natural goodness. But Reformed theology affirms the goodness of creation, and common grace. The world is full of goodness, much of it human. But it persists despite our total depravity and spiritual deadness — it is God's goodness working through the inescapable good design of creation, of which we are a part.

But if by "good" you mean "worthy of God's favor", that's a problem. There is nothing we can do to gain standing before a perfect God, whose standard is "be holy as I am holy". In this sense, there is no goodness in us by which we can claw our way to heaven.