Here's whats on the Lexi:
Brazen Minotaurs:The Brazen Minotaurs are a codex chapter
Minotaurs:The Minotaurs are a chapter of Space Marines, created during the supposedly cursed 21st founding. They have an unusual colour scheme - red and yellow armour quartered, with red and yellow stripes.
The Chapter's tactics are focused entirely on assault, they engage the enemy through direct frontal assaults. Although tactically they are imbalanced, in some situations this works to their favour. The most well-known example of this was the attack on the rebellious Lamenters Chapter during the Badab War. The vicious ship-to-ship combat favored the Minotaurs brutal and direct methodology and the battle ended with the Lamenters' surrender
White Minotaurs:The White Minotaurs are a codex chapter.
As you can see, there's not alot to go on. So you can make up all the fluff you want.