You can try to match it up with these dots and spots,
http://pipephil.eu/logos/en/dots/do-1dot.html
http://pipephil.eu/logos/en/dots/rond-uni.html
...it may simply remain a mystery.
Any other markings on the pipe?
Does it have a stinger? If so, what kind?
Here's a Marxman Super Briar,
dunno if yours could be made by them?
http://www.smokingpipes.com/pipes/estate/united-states/moreinfo.cfm?Product_ID=65015
The best bet would be to find a Dunhill that fits perfectly in the case and you'll have a cool little number!
...or sell the case to me! :P