Kennedy Half Vague Memory

When I was really young like 5 or 6 years old I remember my mom showing me a Kennedy half and telling me I could keep it or spend it. What made it unique besides being a new Kennedy half that had just come out (1964) was I remember it having a really wide rim around it. I've never seen a coin quite like I remember it. From my memory the rim would be at least twice as wide as the coin. I didn't collect until years later so it was quickly converted into candy bars or ice cream cones but I always wondered what kind of error it could have been. In hind site I probably would of ruined it with silver polish a few years later like I did with all my coins until I learned better.
What kind of error would this describe? I have wondered if it was struck from a 1964 Peace dollar planchet.