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 X 1 0 1 1 1 X 1 X 1 X^2 0 1 1 1 0 1 X 1 1 1 X 1 X^2 0 1 1 X 1 1 1 1 0 1 1 0 X X X^2 0 X 0 X 0 0 0 0 0 0 X^2 X X^2+X X^2+X X X X^2+X X^2+X X^2 X^2 0 X X X^2+X X 0 X X 0 X^2+X X X^2 X^2 X^2 X^2+X X^2+X X^2+X X^2+X X X^2+X X^2+X X^2+X X^2+X X^2+X X X^2 X X X^2 X^2+X X^2 0 0 X^2+X X X X X^2 X^2+X X^2 X X^2+X X^2+X X^2+X X^2+X X 0 X^2 X^2 X^2 X 0 X^2+X X X X X^2 0 0 X 0 0 0 X X^2+X X^2+X X X X^2 X X X^2 0 X^2 X^2+X X^2+X X^2+X 0 X X^2+X X^2+X 0 X^2+X X^2+X X^2 X^2 0 0 X^2 X^2 X^2+X X X^2+X X 0 X^2 X X 0 X^2+X 0 0 0 0 X X X X^2+X X X X^2 0 X^2+X X^2+X X^2 0 0 X X^2 X^2 X^2+X X^2+X X 0 X X X X^2+X X X^2 0 X^2 0 0 0 X 0 X X X 0 X^2 0 X X^2+X X^2+X X X^2 X^2 0 0 0 X^2 X^2 X^2+X X X^2+X X X 0 X X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X X 0 X^2 X^2 X^2+X X X X 0 X X^2+X X^2+X X^2 X^2+X X X^2+X X^2+X 0 0 0 X X^2 X^2 0 X 0 X^2+X 0 X^2+X X^2 0 X^2 X^2 X^2 X^2+X 0 X^2 X^2 0 0 0 0 X X X^2 X^2+X X X^2 X 0 X 0 X X X^2+X X^2+X 0 X^2 X X X^2 0 X^2 X^2+X X^2+X 0 X 0 X^2 X X^2+X X 0 X^2+X 0 X 0 X^2+X X X^2 X X 0 X^2 0 X^2 0 0 X^2 X^2+X 0 X^2 X X^2+X 0 X^2+X X^2 X^2+X X^2 X X^2 X^2+X X X^2+X X X X 0 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+105x^66+12x^67+229x^68+48x^69+372x^70+112x^71+447x^72+204x^73+470x^74+264x^75+500x^76+220x^77+339x^78+112x^79+217x^80+36x^81+156x^82+12x^83+96x^84+4x^85+77x^86+42x^88+17x^90+3x^92+1x^112 The gray image is a linear code over GF(2) with n=300, k=12 and d=132. This code was found by Heurico 1.16 in 1.75 seconds.