  Scattered subspaces and $h$-scattered subspaces have been extensively studied
in recent decades for both theoretical purposes and their connections to
various applications. While numerous constructions of scattered subspaces
exist, relatively few are known about $h$-scattered subspaces with $h\geq2$. In
this paper, we establish the existence of maximum $2$-scattered
$\F_q$-subspaces in $V(r,q^6)$ whenever $r\geq 3$, $r\ne 5$, and $q$ is an odd
power of $2$. Additionally, we explore the corresponding MRD codes.
