Right now on the e.l.f. website, receive free shipping on all orders, no minimum required, no code required. This offer includes new items, like the brand new Mattifying Blotting Papers pictured above (click here for more info about those). The e.l.f. email I received did NOT list an end-date for the free shipping promo, so I do not know when it will expire.
PS: Since there's no code required to get free shipping, I tried one of the codes on the Retailmenot site ("22FREE" to get a free mini palette with any $25+ purchase) and it would now allow me to have both the freebie and free shipping. So you cannot combine the free shipping promo with any codes. It's an either/or situation.