The generator matrix 1 0 1 1 1 X^2+X 1 1 X^2 1 X 1 1 1 0 0 1 1 1 X^2+X 1 1 1 X X^2+X 1 X^2 1 1 1 0 1 X 1 1 1 0 1 1 1 1 X 1 1 0 1 1 1 1 X^2 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 X^2 0 X 1 1 1 1 X^2+X 1 0 X X^2 X 1 0 1 1 0 X^2+X+1 1 X+1 X^2+X 1 X^2 1 X^2+1 X X+1 1 1 X^2+X X^2+1 0 1 X^2+1 X+1 X 1 1 X^2+X+1 1 1 X X^2 1 X+1 1 X^2 X^2 1 1 0 X^2+X+1 X^2 X^2+X+1 1 X^2+1 X^2 1 X^2+X+1 X^2 1 X^2+X 1 1 1 X^2 1 1 X^2+X+1 X^2 X^2+1 X^2+X X+1 0 X 1 X+1 X X 1 X X 0 0 1 X+1 1 1 1 X^2+X 0 0 0 X 0 X^2+X 0 X^2 X^2 X X^2+X X^2+X X^2 X X X 0 X^2+X 0 X^2+X X X^2+X X^2 0 X^2 X X 0 0 X^2 X 0 X X X^2+X X^2 0 X X^2+X X 0 X X^2+X X^2+X X X^2 X^2 0 X^2+X X^2+X X^2 0 X 0 X^2 X^2 0 X^2+X X X^2 X^2 X X^2 X 0 X 0 X^2 0 0 X^2 X^2 X^2 X X X^2+X X X 0 0 0 0 X 0 0 0 X^2 X^2 X^2 X^2 0 0 X X X X^2+X X^2+X X^2+X X^2+X X^2+X X X^2+X X^2+X 0 0 X X X 0 X^2 X^2+X X X X^2+X 0 X^2+X X X^2+X X^2 X^2 X^2 X 0 X^2+X X^2+X X^2 X^2 0 X^2 0 X^2 X^2+X X^2+X X^2+X 0 X 0 0 X^2 X X^2 X^2+X X^2 X X X^2+X X^2+X X 0 0 X X^2 X^2+X X^2+X 0 X 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 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 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+36x^70+114x^71+224x^72+230x^73+436x^74+252x^75+446x^76+232x^77+392x^78+214x^79+404x^80+174x^81+339x^82+170x^83+176x^84+74x^85+52x^86+36x^87+18x^88+20x^89+17x^90+10x^91+6x^92+6x^93+4x^94+4x^95+5x^96+3x^98+1x^106 The gray image is a linear code over GF(2) with n=312, k=12 and d=140. This code was found by Heurico 1.16 in 1.33 seconds.