We will discuss the existence of solutions for cubic higher order Schrödinger type equation (NLS) on the whole space with rough initial data. Although such a problem is known to be ill-posed, we show that a randomisation of the initial data yields almost sure local well-posedness. Using estimates in directional spaces, we improve and extend known results for the standard Schrödinger equation in various directions: higher dimensions, more general operators, weaker regularity assumptions on the initial conditions. We will also discuss the existence of invariant measures in the whole space.