The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 X 1 X X 1 X X X 1 1 1 1 X X 1 1 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 generates a code of length 42 over Z2[X]/(X^3) who´s minimum homogenous weight is 28. Homogenous weight enumerator: w(x)=1x^0+115x^28+394x^32+40x^34+843x^36+480x^38+1669x^40+9200x^42+1795x^44+480x^46+870x^48+40x^50+333x^52+102x^56+18x^60+3x^64+1x^72 The gray image is a linear code over GF(2) with n=168, k=14 and d=56. This code was found by Heurico 1.16 in 11.7 seconds.