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 X 0 X 0 0 X X 0 X 0 1 1 1 1 0 1 X X 1 0 1 1 X 1 1 0 1 1 1 1 1 X 1 1 X X X 1 1 0 1 1 X^2 0 X X 1 0 1 X 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 X 0 X^2 0 0 X^2+X X^2+X X X 0 X^2 X^2+X X X^2+X X X X^2+X X^2+X X X^2+X X X^2+X 0 0 X^2+X X X^2+X X^2+X X^2+X 0 X X X^2 X^2+X X X X 0 X^2+X X^2+X X^2+X X^2 X^2+X X X^2 X 0 X^2+X X^2+X X^2 X 0 0 0 X X X^2+X X X 0 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 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 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 X^2 X^2 X^2 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 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 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 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 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 X^2 0 0 X^2 X^2 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 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 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 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 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 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 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 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 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 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 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 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+102x^68+24x^70+403x^72+32x^73+338x^74+168x^75+753x^76+464x^77+564x^78+1064x^79+1054x^80+1472x^81+812x^82+1680x^83+1122x^84+1696x^85+730x^86+976x^87+905x^88+416x^89+474x^90+200x^91+491x^92+16x^93+120x^94+8x^95+172x^96+8x^98+83x^100+2x^102+24x^104+8x^108+1x^112+1x^116 The gray image is a linear code over GF(2) with n=332, k=14 and d=136. This code was found by Heurico 1.16 in 32.7 seconds.