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 X 1 0 1 1 1 1 X X 1 X^2 0 1 1 1 0 1 X 1 1 1 1 0 X^2 1 X 1 X 1 1 1 1 0 1 1 0 0 1 1 1 1 X X 0 X 0 0 0 0 0 0 X^2 X X^2+X X^2+X X X X^2+X X^2+X X^2 X^2 0 X X X^2+X X 0 X X 0 X^2+X X X^2 X^2 X^2 X^2+X X^2+X X^2+X X^2+X X X^2+X X^2+X X^2+X X^2+X X^2+X X X^2 X X X^2 X^2+X X^2 0 0 X^2+X X X X X^2+X X X^2 X^2+X X^2 X^2+X X^2+X X^2+X X 0 X^2 X^2 X^2 X^2+X X X^2 X X^2+X X^2 X X^2+X X^2+X 0 0 X 0 0 0 X X^2+X X^2+X X X X^2 X X X^2 0 X^2 X^2+X X^2+X X^2+X 0 X X^2+X X^2+X 0 X^2+X X^2+X X^2 X^2 0 0 X^2 X^2 X^2+X X X^2+X X 0 X^2 X 0 X X^2+X 0 0 0 0 X X X X^2+X X X^2 X 0 X^2+X 0 X^2 X X^2+X 0 X^2 X^2 X^2+X X^2+X X 0 X X^2 X^2+X X^2 X X^2 0 X^2+X X 0 0 0 0 X 0 X X X 0 X^2 0 X X^2+X X^2+X X X^2 X^2 0 0 0 X^2 X^2 X^2+X X X^2+X X X 0 X X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X X 0 X^2 X^2+X X^2 X X X 0 X X^2+X X^2+X X^2 X^2+X X X^2+X X^2+X 0 0 X^2 X 0 0 X^2 X 0 X^2+X 0 X^2+X X^2 0 X^2 X^2+X 0 0 X^2+X 0 X^2+X X^2+X X 0 0 0 0 X X X^2 X^2+X X X^2 X 0 X 0 X X X^2+X X^2+X 0 X^2 X X X^2 0 X^2 X^2+X X^2+X 0 X 0 X^2 X X^2+X X 0 X^2+X 0 X 0 X^2+X X^2 X X X 0 X^2 0 X^2 0 0 X^2 X^2+X X^2 0 X 0 X^2 X^2+X X^2 X^2+X X^2+X X X^2 X^2+X X X^2+X X X X^2+X X X X^2+X X 0 X^2+X X^2 X 0 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+94x^68+4x^69+284x^70+36x^71+350x^72+108x^73+386x^74+208x^75+541x^76+304x^77+446x^78+228x^79+344x^80+92x^81+202x^82+40x^83+202x^84+4x^85+102x^86+55x^88+44x^90+11x^92+8x^94+1x^96+1x^120 The gray image is a linear code over GF(2) with n=308, k=12 and d=136. This code was found by Heurico 1.16 in 1.78 seconds.