  We present a novel implementation of a genuinely $4^{\rm th}$-order accurate
finite volume scheme for multidimensional classical and special relativistic
magnetohydrodynamics (MHD) based on the constrained transport (CT) formalism.
The scheme introduces several novel aspects when compared to its predecessors
yielding a more efficient computational tool. Among the most relevant ones, our
scheme exploits pointwise to pointwise reconstructions (rather than
one-dimensional finite volume ones), employs the generic upwind constrained
transport averaging and sophisticated limiting strategies that include both a
discontinuity detector and an order reduction procedure. Selected numerical
benchmarks demonstrate the accuracy and robustness of the method.
