yeah, 236' is not really to much gain, especially over 15 miles. I think I may have even done a crit that had close to that every single lap, talk about hurt, after 45 minutes and 20+ laps, I could not see straight. My 60 mile hilly training ride, has over 3,000' of climbing, most of which is made up of short ( <2 mile), steep climbs, and some would not consider this all that hilly.
It sounds as if you are just getting started, 20 miles a day is not to much, just listen to your body. If you keep at it you won't even bother to get the bike out for anything less than 30 miles, atleast I don't.