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We study a geometry associated with rank 3 distributions in dimension 8,whose symbol algebra is constant and has a simple Lie algebra sp(3,R) as Tanakaprolongation. We restrict our considerations to only those distributions thatare defined in terms of a systems of ODEs of the form  $\dot{z}_{ij}=\frac{\partial^2 f(\dot{x}_1,\dot{x}_2)}{\partial\dot{x}_i\partial \dot{x}_j}$, $i\leq j=1,2$. For them we built the full systemof local differential invariants, by solving an equivalence problem a'laCartan, in the spirit of his 1910's five variable paper. The consideredgeometry is a parabolic geometry, and we show that its main invariant - theharmonic curvature - is a certain quintic. In the case when this quintic ismaximally degenerate but nonzero, we use Cartan's reduction procedure andreduce the EDS governing the invariants to 11, 10 and 9 dimensions. As abyproduct all homogeneous models having maximally degenerate harmonic curvaturequintic are found. They have symmetry algebras of dimension 11 (a uniquestructue), 10 (a 1-parameter family of nonequivalent structures) or 9(precisely two nonequivalent structures).

Sp(3,R) Monge geometries in dimension 8