My grandmothers "brown" bread
Googling brown bread Nova Scotia provides a plethora of recipes.  Here are some common traits:


Contains molasses, just as you said
Contains some other grain than simply flour - oatmeal, shredded wheat, and whole grain wheat were among the contenders
Uses shortening to enrich the dough (in some cases butter as well, but shortening was in all recipes)


I'd recommend googling for recipes and picking one which reminds you of your grandmother's.