This paper presents a block BFGS based distributed optimization approach for nonlinear model predictive control (NMPC). The proposed method is a variant of the augmented Lagrangian based alternating direction inexact Newton method (ALADIN), which achieves a locally superlinear convergence rate. To deal with the NMPC problem in continuous time by employing the proposed method, we elaborate on a systematic implementation based on the C++ library PolyMPC. The performance and advantages of the proposed method are illustrated by applying the algorithm to a benchmark continuously stirred tank reactor case study.