You can see the following papers:

S. Majid, *"Quantum Double for Quasi-Hopf Algebras"*,Letters in math. phys., **45**, Number 1 , pages 1-9 (1998).

C. A. S. Young, R. Zegers. *Triangular quasi-Hopf algebra structures on certain non-semisimple quantum groups*, Commun. Math. Phys. 298, 585-611 (2010).