On the classification of finite commutative local rings

In this article we classified up to isomorphism all finite commutative local ring with Jacobson radical $ J $ the index of nilpotency four and conditions:
$$\mathrm{char}\, R=2,\ \dim_{R/J} J/J^2=2,\ \dim_{R/J} J^2/J^3=2,\ \dim_{R/J} J^3=1.$$