Basically it is about getting the all important balance, in your case, with naturally produced Insulin and carbs, type of exercise and the effect it has on you.
I exercise and if low to start with would have a light carby snack or drink, test half way through as well, not just before and after and see what is happening. If too low then you might need to 'fuel' up a bit more.
If a little higher then you could up the intensity and see if it drops. You shouldn't really exercise when your BG level is above around 13 mmol/l as it will tend to make it higher.......something that is not adviseable.
The problem is that exercise can not only raise BG it can also lower it........so, test before, during and after exercise so that you can see what each individual element is doing to you, which is the best way to lower the levels. You may have done too much in this instance. A more leisurely walk might have been better. It also makes a difference as to what other activity between getting up and the walk, a shower perhaps ? This in itself can affect Bg levels.