We give the notion of a CLWX 2-algebroid and show that a  QP-structure (symplectic NQ structure) of degree 3  gives rise to a CLWX 2-algebroid. This is the higher analogue of the result that a  QP-structure of degree 2 gives rise to a Courant  algebroid. A CLWX 2-algebroid can also be viewed as a categorified Courant algebroid. We give a detailed study on the structure of a transitive Lie 2-algebroid and describe a transitive Lie 2-algebroid using a morphism from the tangent Lie algebroid TM to a strict  Lie 3-algebroid constructed from derivations. Then we introduce the notion of a quadratic Lie 2-algebroid and define its first Pontryagin class, which is a cohomology class in H^5(M). Associated to a CLWX 2-algebroid, there is a quadratic Lie 2-algebroid naturally. Conversely, we show that the first Pontryagin class of a quadratic Lie 2-algebroid is the obstruction class of the existence of a CLWX-extension.