Pre-runtime scheduling of avionic systems is used to ensure that the systems provide the desired functionality at the correct time. This paper considers scheduling of an integrated modular avionic system which from a more general perspective can be seen as a multiprocessor scheduling problem that includes a communication network. The addressed system is practically relevant and the computational evaluations are made on large-scale instances developed together with the industrial partner Saab. A subset of the instances is made publicly available. Our contribution is a matheuristic for solving these large-scale instances and it is obtained by improving the model formulations used in a previously suggested constraint generation procedure and by including an adaptive large neighbourhood search to extend it into a matheuristic. Characteristics of our adaptive large neighbourhood search are that it is made over both discrete and continuous variables and that it needs to balance the search for feasibility and profitable objective value. The repair operation is to apply a mixed-integer programming solver on a model where most of the constraints are treated as soft and a violation of them is instead penalised in the objective function. The largest solved instance, with respect to the number of tasks, has 54,731 tasks and 2530 communication messages.