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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 1 1 1 1 1 1 1 0 1 1 X 1 1 1 1 1 1 X X 1 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X X^2 X^2+X X^2+X 0 X^2+X 0 X^2 X 0 X^2+X X X^2 0 X^2+X X^2 X 0 X^2+X X X^2 X^2+X 0 0 X^2+X X^2 X X^2 X X^2+X X^2+X 0 0 X X^2 0 X X^2+X X^2 0 X^2+X 0 X^2+X X^2 X 0 0 X^2 X^2+X X^2+X X^2+X X 0 X^2 0 X^2 X^2 X^2+X X 0 X^2 X^2 X^2+X X 0 X^2 X^2+X X^2+X 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 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 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 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+16x^70+84x^72+122x^74+64x^75+94x^76+384x^77+52x^78+64x^79+26x^80+44x^82+26x^84+20x^86+24x^88+2x^90+1x^144 The gray image is a linear code over GF(2) with n=308, k=10 and d=140. This code was found by Heurico 1.16 in 0.401 seconds.