  Let k be an algebraically closed field of characteristic two. Let R be the
ring of Witt vectors of length two over k. We construct a group stack \hat G
over k, the metaplectic extension of the Greenberg realization of Sp_{2n}(R).
We also construct a geometric analog of the Weil representation of \hat G, this
is a triangulated category on which \hat G acts by functors. This triangulated
category and the action are geometric in a suitable sense.
