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 1 0 X^2 1 1 1 1 1 X^2 1 1 1 1 1 1 1 0 X 1 1 1 X 1 X 1 X^2 1 1 1 0 1 X 0 1 1 1 X X 1 1 0 X 0 0 0 X X^2+X X X^2 X^2 X 0 0 X X X^2+X 0 0 X^2+X X X^2 X X^2+X X^2 X^2 0 X^2 X X^2+X X 0 X^2+X X X^2+X X^2 0 X X^2 X^2+X X^2 X X^2 X^2+X X^2 X^2 X^2+X X X^2+X 0 X X 0 X^2+X X^2+X 0 0 0 X 0 X X^2+X X^2+X 0 0 X^2+X X^2 X^2 X X X^2+X 0 X^2+X X X^2 X^2 X 0 X 0 0 X 0 X X X 0 X^2 0 X^2+X X X^2+X 0 X^2+X 0 X^2 X^2+X X^2 X^2+X 0 X^2 X X 0 0 X X X^2 X^2+X X X^2 0 0 X 0 X^2 X X X X^2 X^2+X X^2+X X^2+X X 0 X^2+X X X 0 X X^2+X X^2 X^2+X 0 X X^2 X^2+X X^2 X^2+X X^2 X X^2 X 0 0 0 X X X^2+X X X^2 X 0 X^2+X X 0 X 0 0 0 X X 0 X X^2+X 0 X X^2 X X^2 X^2+X X 0 X^2 X X 0 X^2+X X^2 X^2+X X^2 X^2+X 0 X X^2+X 0 0 X^2 X X^2+X X^2+X 0 0 0 X^2+X X 0 X^2+X X^2+X X X^2+X X^2 0 0 X^2 X^2 0 X^2+X X^2 X^2+X 0 X X X X^2 X^2 X X^2 X 0 X^2+X X^2 X^2 X X^2+X X^2 0 X X^2 X X X^2+X X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 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 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 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+37x^70+66x^71+91x^72+98x^73+127x^74+162x^75+195x^76+224x^77+176x^78+182x^79+170x^80+146x^81+117x^82+84x^83+30x^84+20x^85+35x^86+12x^87+22x^88+16x^89+19x^90+6x^91+2x^92+8x^93+1x^100+1x^130 The gray image is a linear code over GF(2) with n=312, k=11 and d=140. This code was found by Heurico 1.16 in 0.674 seconds.