Multigrid methods are fast and scalable numerical solvers for partial differential equations (PDEs) that possess a large design space for implementing their algorithmic components. Code generation approaches allow formulating multigrid methods on a higher level of abstraction that can then be used to define a problem- and hardware specific solution. Since these problems have considerable implementation variability, it is crucial to define a general mapping of core components in multigrid methods to the target software. With SYCL there exists a high-level C++ abstraction layer that is capable of targeting a multitude of possible architectures. We contribute a general way to map multigrid components to SYCL functionality and provide a performance evaluation for specific algorithmic components.