You don't mention your age nor do you mention your activity level prior to this point. Nor do you say what kind of BMI you might be- (basically are you overweight?). I recommend, especially since you just stopped smoking 6 weeks ago, that you get a complete check-up at your doctors. If your MD gives you a relatively clean bill of health you need to do a test ride- just as someone recommended. Do the ride on a day off from work. This will give you the chance to see how long it will take, what the ride is like traffic-wise and how you feel afterwards.

If your job is physically stressful you're pushing the mileage for an every day commute. See how hungry you feel, will you have the energy to do a full day of work and then ride home? What about bad weather, wind, mechanical difficulties (esp flat tires). What will you need to carry with you? Are there other options- trains, buses, car pooling?

I think you might find doing a commute of this length 2 or 3 times a week at first might be more than enough. It's doable, it's on the high end of weekly commute mileage but it's doable with perseverance and commitment. Good luck- let us know how it goes!