The generator matrix 1 0 0 1 1 1 0 1 1 1 X^2+X 1 0 X^2 1 1 1 X^2+X 1 X X X^2+X X^2+X 1 1 1 1 0 X^2 1 X 1 1 1 0 X 1 X 0 X^2 1 1 1 1 1 1 X^2 1 1 X 1 1 X^2+X 1 1 1 1 1 1 1 1 1 0 X^2 1 1 0 1 1 X^2 1 0 1 0 0 1 1 1 X^2 X^2+X+1 X+1 1 X 1 X^2+X X^2+X X^2+X+1 X^2+X 1 1 X^2+X 1 0 1 X^2+X 1 X+1 X^2 1 X^2+X X^2+X 1 X^2+1 X^2+1 X 1 0 X^2+1 1 0 1 X^2+X+1 0 X^2 X^2+X+1 0 X 1 X X^2 1 X+1 X^2+X+1 1 X^2+1 X X^2 1 1 X^2+1 X^2+1 X^2+X X^2+1 0 1 1 X+1 X X X 1 0 0 0 1 X+1 X^2+X+1 0 X+1 X X^2+X X^2+X+1 X^2+X+1 X^2+1 X^2+X 1 X^2 1 X+1 X^2 X 1 1 1 X^2+X X^2+X 1 0 X^2+1 X^2+X+1 1 X^2+1 X^2+1 X^2+1 X^2+X X X 1 1 0 1 X^2+X+1 X^2 X^2+X+1 X^2+X+1 1 1 X^2 X X^2+1 X^2+1 X^2+X+1 0 X^2+1 0 X^2+X+1 X^2+1 X^2 0 X^2+X X+1 1 X^2+1 X^2+1 1 1 X^2 0 1 X+1 X X^2+X 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 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 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 0 0 0 0 X^2 generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+50x^64+174x^65+262x^66+406x^67+414x^68+384x^69+375x^70+304x^71+376x^72+306x^73+246x^74+216x^75+148x^76+126x^77+91x^78+80x^79+59x^80+32x^81+15x^82+18x^83+6x^84+2x^85+2x^86+2x^88+1x^90 The gray image is a linear code over GF(2) with n=284, k=12 and d=128. This code was found by Heurico 1.16 in 0.91 seconds.