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 X^2 X X 0 X X 0 1 0 0 1 1 1 1 1 X^2 1 X^2 0 1 X^2 1 X^2 1 1 0 0 1 X 1 X^2 X^2 1 1 X X^2 1 0 X 0 0 X 0 0 0 0 0 0 X^2 X^2 X X^2+X X 0 0 X^2 X^2+X X^2+X X X X X 0 X X^2+X X 0 X X^2+X X^2 X^2+X X^2 X^2 X^2+X X 0 0 X X^2 X X^2 X^2 X^2+X X^2 0 X X^2 X 0 X X^2+X 0 X^2 X X 0 X^2 X^2 0 X^2 X^2 X^2+X X^2 0 X^2 X 0 X X^2 X X^2+X X X X X^2 X X^2+X X 0 0 X 0 0 0 0 0 0 0 0 0 X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X X^2 X^2 X^2+X X^2+X 0 0 X X X X^2+X X^2+X X^2+X X^2 X^2 X^2+X X X X^2 X X^2+X X 0 0 X X^2 0 X^2 X 0 X^2 X^2+X 0 X^2 X^2+X 0 X^2 X X^2+X X X^2+X X 0 X^2 X^2 X^2 X X X X^2 X^2 X 0 0 X^2 X 0 X^2 0 0 0 0 X 0 0 X^2 X^2+X X X X X X^2 X^2+X X X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X X^2+X X X^2 X X^2+X X^2+X X X^2+X 0 X^2 0 0 0 X^2+X 0 0 X^2+X X X 0 0 X X^2 0 0 0 X^2+X X X^2+X X 0 X 0 X^2+X X^2 X X^2 X^2+X 0 0 X 0 X^2 X^2 0 X^2 X^2 0 X^2+X X^2+X X 0 X^2 X 0 0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X 0 X X 0 X^2 X 0 X^2+X X^2+X X X^2+X X X^2 X^2 X X^2 X^2 0 X^2+X X^2 0 X^2+X X X^2+X X^2 0 X^2+X 0 X^2+X 0 0 0 X X X X^2+X 0 0 0 0 0 X^2+X X^2 X^2+X X^2 X^2+X 0 X^2 X^2 X^2 X^2+X 0 X X^2+X X^2+X X X X^2 X^2+X X^2+X 0 X X 0 X^2 X^2 0 0 0 0 0 X X X^2 X^2+X X X^2+X X^2 X X 0 X 0 X^2+X X^2+X 0 X X^2 X^2 X^2+X X^2 X X^2+X X^2+X X^2 X X^2 X^2 X^2+X 0 X X^2+X 0 0 X^2 X^2 0 X^2 X^2+X X X^2 0 X 0 X^2 0 X^2 X 0 0 X^2+X X 0 X 0 X^2 X^2+X 0 X^2+X X 0 X^2+X X^2+X X^2 0 0 X X 0 X^2 X^2+X X^2 X X generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+186x^68+12x^69+394x^70+68x^71+607x^72+188x^73+720x^74+304x^75+765x^76+472x^77+976x^78+444x^79+768x^80+304x^81+662x^82+172x^83+419x^84+44x^85+296x^86+32x^87+178x^88+4x^89+100x^90+4x^91+45x^92+18x^94+6x^96+2x^98+1x^108 The gray image is a linear code over GF(2) with n=312, k=13 and d=136. This code was found by Heurico 1.16 in 7.24 seconds.