Try something like this.
1. Walk for 2 minutes 30, jog for 30 seconds repeat for maybe 7-8 times. So you're doing 21-24 minutes at a time.
2. Do this 5 days a week, making sure not to have the two days off back to back, so make sure when you have a day off, your have the other 3 days later, so the days are nicely spaced.
3. Week 2. Walk for 2 minutes 20, jog for 40 seconds.
4. Week 3. Walk for 2 minutes 10, jog for 50 seconds.
Keep cutting walking times by 10 seconds every week, and increase jogging by 10 seconds every week.
This should give you the chance to see how much exertion you can do, and over time you might be able to do the 20 minutes jogging completely.