Rephrase the question to "would it be right for a 22 year old man to marry a forty-four year old widow?" "Dating" is only right when done in the pursuit of marriage. If you're asking if it would be right for you to romantically entertain her without any consideration of marrying her, that answer is no and it is no regardless of age. But assuming that what you're really asking is if it would be morally OK to marry this woman, the answer is "yes" in a vaccuum, but:
Why would you do that? It is probable that you will have no children with her. If you do not want children, then why are you getting married at all? If you want "companionship" there are ways to do that without marriage-- make some friends, get a dog, etc. If you can't do that, then you're not mature enough to get married to anyone anyways.
As someone else pointed out, if this woman is forty four and traditional Catholic (and widowed to boot), it's a sure bet she has children. Probably some that are close to your age! Are you ready to be their foster-father? Can you provide good moral and practical advice to a young man only four years younger than yourself? What of her daughters? They'll be much closer to your own age than she will be. That alone could be a problem.
And as someone else said, are you financially stable? Most 22 year olds aren't. Even if you are, how will you feel supporting a family that isn't yours? A wife who cannot bear you children? There are some very virtuous men out there who have done exactly this. But let's not pretend like there isn't quite a bit of potential in a situation like this for resentment. There is. And you'll be spending the rest of your life with her.