We don't have genes that kill us. These are genes that control all the repair and defense systems that protect our cells from harm. That is why we age, but some of us are better protected than others. That's an interesting question. Let's look first at what the animal kingdom tells us.
Different species have different life spans.
I believe that this is fundamentally due to differences in genes. In principle, there is no reason why the protection we humans enjoy cannot be improved still further. Understanding what genes do for aging tells us the nature of the systems we are up against, but it may be a long time before gene therapies are available and there are huge ethical issues. However, once we recognize that aging is caused by damage that builds up, we can try to boost our body's existing defense mechanisms through nutrition, lifestyle and so on. There is a lot of evidence that attack by free radicals is an important contributor to aging.