Geodesic
Local rings of order $p^6$ with $4$-nilpotent radical of Jacobson
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 3 (2006), pp. 15-59

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The structure and classification up to isomorphism of all finite local rings of order $p^6$ with characteristics $p$ and $4$-nilpotent Jacobson radical are determined. 
@article{SEMR_2006_3_a1,
     author = {E. V. Zhuravlev},
     title = {Local rings of order $p^6$ with $4$-nilpotent radical of {Jacobson}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {15--59},
     publisher = {mathdoc},
     volume = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2006_3_a1/}
}
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E. V. Zhuravlev. Local rings of order $p^6$ with $4$-nilpotent radical of Jacobson. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 3 (2006), pp. 15-59. http://geodesic.mathdoc.fr/item/SEMR_2006_3_a1/