The generator matrix 1 0 0 1 1 1 0 1 1 1 X X^2 1 X^2 1 X^2+X 1 1 X^2+X 1 X^2+X 1 1 0 1 1 X^2 X^2+X 1 X 1 X 1 1 1 X^2+X 1 X X^2 1 1 0 X^2 1 0 X X^2+X 1 1 1 1 1 1 1 1 X^2+X 1 X^2+X 0 0 X^2 X 1 X^2+X 1 1 1 1 1 1 1 1 1 1 X^2 1 1 0 1 0 0 1 1 1 X^2 X^2+X+1 X+1 1 1 X X^2+X X^2+1 1 X^2+X+1 X X^2+X X^2+X 1 1 0 1 X X^2+X+1 1 X^2 X^2+X+1 1 X^2+1 X X^2+X X^2+X 0 1 X^2+X+1 1 X^2+X X+1 X^2+1 X 1 0 1 X^2 1 X^2+1 X^2+X X X+1 1 X^2+X+1 X^2+X 1 X 1 X 1 1 1 0 X^2+X 1 1 X^2+X+1 X^2 X+1 X X^2 X X^2 X^2+1 1 1 1 0 0 0 1 X+1 X^2+X+1 0 X+1 X X^2+X X^2+X+1 X^2+1 X 1 1 X^2+1 X^2+X+1 X^2 0 1 X+1 0 X 1 X^2 0 X 1 1 1 X^2+X+1 1 1 X+1 X^2+X 1 X X+1 X^2+1 1 X^2 X^2+1 1 1 X^2+X X^2 1 X X^2+X+1 X^2+1 X 0 X 0 X^2+1 0 1 X+1 1 X^2+1 1 X^2+X 1 X^2+X+1 X^2 X^2 X X^2 X^2+1 X+1 X^2+X+1 X^2+1 1 0 1 X^2+1 X^2+1 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 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 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 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 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 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+57x^70+182x^71+258x^72+534x^73+290x^74+484x^75+209x^76+422x^77+231x^78+350x^79+203x^80+280x^81+142x^82+154x^83+70x^84+84x^85+43x^86+44x^87+14x^88+18x^89+4x^90+2x^91+13x^92+6x^93+1x^94 The gray image is a linear code over GF(2) with n=308, k=12 and d=140. This code was found by Heurico 1.16 in 1.05 seconds.