  A class of anyonic models for universal quantum computation based on
weakly-integral anyons has been recently proposed. While universal set of gates
cannot be obtained in this context by anyon braiding alone, designing a certain
type of sector charge measurement provides universality. In this paper we
develop a compilation algorithm to approximate arbitrary $n$-qutrit unitaries
with asymptotically efficient circuits over the metaplectic anyon model. One
flavor of our algorithm produces efficient circuits with upper complexity bound
asymptotically in $O(3^{2\,n} \, \log{1/\varepsilon})$ and entanglement cost
that is exponential in $n$. Another flavor of the algorithm produces efficient
circuits with upper complexity bound in $O(n\,3^{2\,n} \, \log{1/\varepsilon})$
and no additional entanglement cost.
