  The Grassmannian $V_2(\mathbb{R}^{n+2})$ of oriented 2-planes in $\mathbb
R^{n+2}$ where $n\ge3$ carries a homogeneous parabolic contact structure of
Grassmannian type. The main result of this article is that on
$V_2(\mathbb{R}^{n+2})$ lives an elliptic complex of invariant differential
operators of length 3 which starts with the 2-Dirac operator and that the index
of the complex is zero.
