I think the important thing to remember in all this is that we do good works not in order to get to heaven but rather we do them because that is what we long to do if we know God’s love for us: to show that love to others. Well Clement sums it up much better.
… And we, too, being called by His will in Christ Jesus, are not justified by ourselves, nor by our own wisdom, or understanding, or godliness, or works which we have wrought in holiness of heart; but by that faith through which, from the beginning, Almighty God has justified all men; to whom be glory for ever and ever. Amen. What shall we do, then, brethren? Shall we become slothful in well-doing, and cease from the practice of love? God forbid that any such course should be followed by us! But rather let us hasten with all energy and readiness of mind to perform every good work. For the Creator and Lord of all Himself rejoices in His works. For by His infinitely great power He established the heavens, and by His incomprehensible wisdom He adorned them. He also divided the earth from the water which surrounds it, and fixed it upon the immoveable foundation of His own will. The animals also which are upon it He commanded by His own word into existence. So likewise, when He had formed the sea, and the living creatures which are in it, He enclosed them [within their proper bounds] by His own power. Above all, with His holy and undefiled hands He formed man, the most excellent [of His creatures], and truly great through the understanding given him-the express likeness of His own image. For thus says God: "Let us make man in Our image, and after Our likeness. So God made man; male and female He created them." Having thus finished all these things, He approved them, and blessed them, and said, "Increase and multiply." We see, then, how all righteous men have been adorned with good works, and how the Lord Himself, adorning Himself with His works, rejoiced. Having therefore such an example, let us without delay accede to His will, and let us work the work of righteousness with our whole strength.
From Clement’s letter to the church at Corinth chapters XXXII-XXXIII