On unit group of a finite local rings of characteristic $p$

We describe the structure of the unit group of a commutative finite local rings of characteristic $p$ with Jacobson radical $J$ such that ${\dim_F J/J^2=3}$, ${\dim_F J^2/J^3=1}$, ${\dim_F J^3=1}$, $J^4=(0)$ and $F=R/J\cong GF(p^r)$, the finite field of $p^r$ elements.