You were wise to stop when you did.
Once you past 12 minutes, what was a brisk march up hill, turns into a jog/run.
Hardly wise unless you a member of an athletics club! You need to preserve your knees etc.
Look up the BRUCE protocol for speeds/slope.
I think a mimimum of nine minutes is required although I have heard that some conditions require 12 minutes.
Speak to your AME for the definitive answer.