Same for me although most of the time not up to 14. It is somewhat of a known phenomenon, if you exercise lightly (walking) your BG goes down, if you exercise hard it goes up. Just your body reacting to the need for energy and yes it will use any available glucose from the liver and muscles first before switching to fat burn or if you really working hard anaerobic mode.
For me as a T2 this means that after 45 minutes to an hour+ my BG goes down pretty steep to a normal level again.
Don't know how a T1 should handle this though.