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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 X X 0 X X X 1 X 1 1 X^2 1 1 X X X^2 0 1 1 X X X 1 1 1 1 1 X 1 X 1 1 1 1 1 0 X 0 0 0 0 0 0 X^2 X^2 X X^2+X X 0 0 X^2 X^2+X X^2+X X X X X 0 X X^2+X X 0 X X^2+X X^2 X^2+X X^2 X^2 X^2+X X 0 0 X X^2 X X^2 X^2 X^2+X X^2 X^2 X X^2+X X^2 X X^2 X^2+X X^2+X X X^2+X 0 X^2 X X X X X^2+X X^2+X 0 0 X^2+X X X^2 0 0 X X^2+X 0 X X^2+X 0 0 X 0 0 0 0 0 0 0 0 0 X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X X^2 X^2 X^2+X X^2+X 0 0 X X X X^2+X X^2+X X^2+X X^2 X^2 X^2+X X X X^2 X X^2+X X 0 0 X X^2 X^2 X^2+X X X^2 X^2 0 X^2 X^2+X 0 X X^2 X X X^2+X X^2 X X^2+X X X^2+X X^2+X X X X^2+X X^2+X X 0 0 X^2+X X 0 0 0 X 0 0 X^2 X^2+X X X X X X^2 X^2+X X X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X X^2+X X X^2 X X^2+X X^2+X X X^2+X 0 X^2 0 0 0 X^2+X 0 0 X^2+X X X 0 X 0 X^2 X^2 X^2+X X X^2 X^2 X X X^2 X^2 0 X X^2 X^2+X 0 0 X 0 0 X X X^2+X X X^2 X^2+X 0 X^2 X^2+X 0 0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X 0 X X 0 X^2 X 0 X^2+X X^2+X X X^2+X X X^2 X^2 X X^2 X^2 0 X^2+X X^2 0 X^2+X X X^2+X X^2 0 X^2+X 0 X^2+X 0 0 0 X^2 X 0 X^2+X 0 X^2+X X^2 X^2 0 X^2+X 0 X 0 X X^2 X^2+X X^2 0 0 X^2+X X X^2+X X^2 0 X X X^2+X X^2 X X^2+X 0 0 0 0 0 X X X^2 X^2+X X X^2+X X^2 X X 0 X 0 X^2+X X^2+X 0 X X^2 X^2 X^2+X X^2 X X^2+X X^2+X X^2 X X^2 X^2 X^2+X 0 X X^2+X 0 0 X^2 X^2 0 X^2 X^2+X X X X^2 X^2 X^2+X X^2 X^2 0 X^2+X X^2 X^2+X 0 X X^2+X 0 X^2 X^2+X X 0 X^2+X X^2 0 X 0 X X^2 X^2+X X X^2 X^2+X X^2+X generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+146x^64+396x^66+36x^67+579x^68+128x^69+650x^70+292x^71+903x^72+560x^73+994x^74+576x^75+841x^76+308x^77+644x^78+116x^79+420x^80+24x^81+224x^82+4x^83+189x^84+4x^85+82x^86+49x^88+18x^90+7x^92+1x^112 The gray image is a linear code over GF(2) with n=296, k=13 and d=128. This code was found by Heurico 1.16 in 6.54 seconds.