It is true that there are rewards above and beyond eternal life and that eternal life is a gift of grace, but Scripture plainly teaches that eternal life itself is a reward or fruit of our good deeds.
One passage which spells this out is Galatians 6:7-10: "Whatever a man sows, that he will also reap. For he who sows to his own flesh will from the flesh reap corruption, but he who sows to the Spirit will from the Spirit reap eternal life. So let us not grow weary in well-doing [Gk, "working good"], for in due season we will reap, if we do not lose heart. So then, as we have opportunity, let us do good [Gk, "work good"] to all men, and especially to those who are of the household of faith."
In this passage Paul states that "eternal life"--not just unspecified "rewards"--is the harvest "reaped" as a result of "sowing to the Spirit" through "well-doing" or "doing good to all men."
One might press the analogy by pointing out that the harvest is still a "gift" of God, since the act of sowing does not make the seed alive or cause it to grow. The act of sowing undeniably leads to the harvest, and the same is true of our good deeds and eternal life.