Dan O'Day gives a good analysis of the Greek in his answer, but I find his conclusion to be quite surprising on the basis of what he said.
Life in the New Testament (and in a more hidden way, in the old) overwhelmingly speaks of eternal life; that is, the eternal communion with God into which we enter by grace through Jesus Christ. Where do I even begin to cite for that? I want to quote the entire Gospel of John right here!
Moreover (which Dan seems to acknowledge) heir has to do with the hope (as Soldarnal points out in the question) of receiving the grace of God (eternal life). Once again, this usage is overwhelming in the New Testament, and once again, in a more hidden way, in the Old.
In combination, this is a powerful argument. I would charge any one you to find an example of when heir, grace, and life in conjunction, or even two of them in conjunction, mean anything other than the hope of eternal life.
But think about the logic of this passage. If Peter says, "Treat your wife in an understanding way; after all, she's your wife," that is an okay argument, but really is not very strong. But "Treat your wife in an understanding way. She has as much claim to the kingdom of God as you do—and more than you if you treat her wrongly, for then you forfeit your own claim," is an extremely weighty argument. Whereas the first is an appeal to common sense, which are badly muted by sin and a sinful culture, the second is a powerful theological appeal. Any man who abuses his wife knows that she's his wife. But if she is his equal before God, bought with the blood of Christ, loved by God in the same way as he is, and following the logic out to its necessary conclusion, equally human (revolutionary in the ancient world), equally made in the image of God—that is far more powerful.
The grace of life is certainly eternal life.