not register the correct mileage while running

Which Garmin model are you using?

Kitty van Os said:

he indicates that I walk more than in reality

If you're using the Move IQ feature, perhaps you should try setting the timed threshold so the watch knows when you're running.

vívoactive 4/4S - Activity Tracking Settings (garmin.com)

Auto Activity Start
Allows your device to create and save timed activities automatically when the Move IQ feature detects you are walking or running. You can set the minimum time threshold for running and walking.

Thanks for the tip! I’ll hope this helps ️