Washington Post: "Running a marathon at a pace of 10 minutes per mile releases about 5 percent fewer carbon dioxide equivalents than running at six minutes per mile"

Running a marathon: How green are our two legs? - The Washington Post

A calorie from fruit and vegetables is responsible for about 40 percent less greenhouse gas than a meat or dairy calorie, so vegan runners do substantially better in this department than omnivores.

You could also slow down. While slower runners get less glory, the tortoises are a little bit greener than the hares. Running a marathon at a pace of 10 minutes per mile releases about 5 percent fewer carbon dioxide equivalents than running at six minutes per mile.
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You might be surprised at how these totals compare to driving. The EPA estimates that the average vehicle on American roads emits 0.87 pounds of carbon dioxide per mile. So, over 26.2 miles, a car would account for just 22.8 pounds of greenhouse gas — about 19 percent more than the runner.