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 0 1 1 1 1 1 1 1 1 1 X^2 1 X^2 1 1 1 1 X 1 0 1 1 1 0 1 1 1 X 1 X^2 1 X 1 X 1 X 1 X 1 X 0 X 0 0 0 X X^2+X X X^2 X^2 X^2+X 0 X^2+X X^2 X^2+X X X^2 0 X^2+X X^2+X X^2 0 X^2+X X^2+X 0 X 0 X^2+X 0 X^2 X X^2+X 0 X^2 X^2+X X^2+X 0 X X X^2 X^2+X X^2+X 0 X X X^2+X 0 X^2 0 X X^2+X X^2 X^2+X X^2+X 0 X^2 X^2 0 X^2+X 0 0 X 0 X^2+X 0 X^2 X X^2 X X^2+X X X^2 X X^2 0 X^2 X^2+X 0 0 X 0 X X X 0 X^2 0 X^2+X X^2+X X^2 X X X^2 0 X^2+X X X^2 X^2+X X^2 X X^2 X X^2 X^2+X X X^2 X^2 X^2+X X^2 0 0 X X^2 X X X^2+X X X^2 X^2+X X^2+X 0 X^2+X X^2+X X X X^2+X X^2+X X^2 X^2 X 0 X^2+X X^2+X 0 X^2+X X X^2 X X^2 0 0 X^2 X^2+X 0 X 0 X X^2+X 0 X^2 0 X X^2 X^2 0 0 0 X X 0 X X^2+X 0 X X^2 X^2 X X^2+X X^2+X 0 X X^2 0 X X^2 X^2 X X^2 X^2+X 0 X^2+X 0 0 X^2+X X X 0 X^2+X X^2 0 X^2+X X X X^2 X^2 0 0 X X^2 X^2+X X^2+X X X 0 X^2+X X^2 X^2 0 0 X X 0 X^2 X^2+X X^2 X X^2+X X^2+X X 0 0 0 X^2+X X^2 0 X^2 0 X^2 X X^2+X 0 0 0 0 0 X^2 0 0 0 X^2 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 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 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 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+134x^70+8x^71+195x^72+52x^73+233x^74+124x^75+243x^76+152x^77+301x^78+112x^79+155x^80+52x^81+103x^82+12x^83+71x^84+35x^86+32x^88+24x^90+6x^92+2x^94+1x^128 The gray image is a linear code over GF(2) with n=308, k=11 and d=140. This code was found by Heurico 1.16 in 1.99 seconds.