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 X 0 X 0 0 1 1 1 X X 0 1 1 X 0 X 1 1 0 1 1 1 1 X 0 0 1 1 1 1 X 1 1 X 0 1 1 1 X^2 1 0 X^2 X^2 1 1 X 1 X X 1 1 1 1 X 1 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2+X X^2 0 X^2+X X X^2 X^2+X 0 X^2+X 0 X^2 X X^2+X 0 0 X X^2+X X X^2+X X X X^2+X 0 X^2 X^2+X X^2+X X X^2+X 0 X^2+X X X^2+X 0 X^2+X X X^2 X^2 X X^2 X^2+X X X X^2+X 0 0 X X^2+X X 0 X^2+X X X^2+X X^2 X X^2 X^2 X X X X^2+X X X X X X^2+X X^2+X X X X^2+X X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+100x^68+36x^70+307x^72+4x^73+214x^74+92x^75+666x^76+300x^77+520x^78+692x^79+945x^80+1288x^81+764x^82+1720x^83+1145x^84+1720x^85+766x^86+1288x^87+923x^88+692x^89+526x^90+300x^91+632x^92+92x^93+212x^94+4x^95+248x^96+32x^98+98x^100+2x^102+38x^104+14x^108+2x^112+1x^116 The gray image is a linear code over GF(2) with n=336, k=14 and d=136. This code was found by Heurico 1.16 in 34 seconds.