The DXY is not a measure of US dollar strength. It is a measure of how the US dollar is trading against other similarly failing fiat currencies (Euro, Pound, Yen, etc.).

The true measure of US dollar strength is how many of them it takes to buy an ounce of gold. At the moment, it takes about 3,350 of them, or roughly 100 times more than it did when Nixon closed the gold window.