  The polar orthogonal Grassmann code $C(\mathbb{O}_{3,6})$ is the linear code
associated to the Grassmann embedding of the Dual Polar space of $Q^+(5,q)$. In
this manuscript we study the minimum distance of this embedding. We prove that
the minimum distance of the polar orthogonal Grassmann code
$C(\mathbb{O}_{3,6})$ is $q^3-q^3$ for $q$ odd and $q^3$ for $q$ even. Our
technique is based on partitioning the orthogonal space into different sets
such that on each partition the code $C(\mathbb{O}_{3,6})$ is identified with
evaluations of determinants of skew--symmetric matrices. Our bounds come from
elementary algebraic methods counting the zeroes of particular classes of
polynomials. We expect our techniques may be applied to other polar Grassmann
codes.
