Running is done by pressing the " key, by default.
It costs a lot more stamina, however, and Leg and Feet Encumbrance increases how many Movement points it costs to Run.
There’s also the Trait “Fleet-Footed”, which increases your Movement Speed by 15% on sure footing. “Quick” gives you more Points to use per round.
EDIT: This will help you escape zombies, but they’ll still see you. If you want to avoid detection, you should try taking the “Night Vision” trait and raiding at night. I’ve never tried it, but it seems to work for some people.