You have to be careful if your blood sugar is above 14 and you exercise. You could make ketones which is a sign you are not getting enough insulin and you risk DKA. If you are waking to 12.6 are you getting DP (dawn phenomenom) and that is causing it? Or are you going to bed high? You might try to figure out why your levels are high when you wake. Are you a newer type1 ? Because as time goes on you make less and less insulin and you will need more. Of course DP causes it and people take a correction dose to deal with that. There is also FOTF (foot on the floor) that when you wake or a certain time after you wake your BG levels rise too. Both DP and FOTF are caused by hormone releases. And you can have both,
Normally walking doesn't increase BG levels. Strength or harder exercise can. But sometimes length of time you exercise can increase BG levels as your liver tries to provide fuel. And since we don't make our own insulin to deal with that your BG level goes up. But like I said normally walking isn't likely to cause that. Maybe it's a combo of not enough insulin in the first place and length of time walking??? But that's a guess.