I'd say it's possible if you stay dedicated, keep it slow and are lucky with injuries. I'd aim for 4m today, then 5,6,7,8,9,10 over the next six Sundays. If you get do 10 in training you should be able to do 13.1 in the race. You could even do a couple of 12m runs in weeks 7 and 8, and have a 2 week taper into the event.
Remember to do shorter runs during the week, keep everything nice and slow, and focus on doing everything right - warm up, cool down, stretching after exercise, and you can do it!