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 X^2 X^2 X^2 0 X 0 1 1 0 X^2 0 X X^2 1 X X X 1 1 X 0 X X^2 1 0 X 1 1 X 1 X X X^2 1 X X 1 0 X 1 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X 0 X^2+X X X^2 X^2+X X^2+X 0 0 X X^2+X X^2 X^2 0 0 X^2+X X X^2+X 0 0 0 X^2 0 X X^2+X X X^2 X X^2+X X X X X X X^2+X X X^2 X^2 0 0 X^2 X^2 0 0 X X^2 X X^2 X^2+X X X 0 X^2 X^2+X X X 0 0 X^2+X X^2+X X 0 0 X^2 X^2 X^2+X X X X X^2 0 0 X 0 X X X^2+X 0 0 0 X X^2 X X^2+X X^2 X^2+X X^2 X^2 X^2 0 X X X^2+X X X X X^2+X X^2 X^2 X X^2 X^2+X 0 X^2 X^2 X^2 X X X^2 X^2+X 0 X X 0 X X^2+X X X^2+X 0 0 X X X X X 0 0 X^2 X^2+X X^2+X 0 X^2 0 X^2+X X X^2+X X^2 0 X X^2 X^2+X X^2 0 X^2 X X^2+X X X^2 X^2+X X^2+X X X^2 0 0 0 X X 0 X^2+X X 0 X 0 X X^2+X X^2+X X^2 X^2 0 X^2 X X^2+X 0 0 X^2+X X 0 0 X X^2+X 0 X X X 0 X^2 0 X^2+X X^2 0 X X^2 0 X^2+X X^2 X X^2 X^2+X X^2+X X X^2+X X^2 X^2 X^2+X 0 X^2 X^2+X X X^2+X X^2+X X^2 X X^2 X^2 0 X^2 X^2+X X^2 X X^2+X X^2 X^2+X X X^2 0 X X^2 0 X 0 X^2+X X^2+X 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 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 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 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 X^2 0 0 0 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+169x^70+8x^71+489x^72+44x^73+699x^74+200x^75+1061x^76+352x^77+1203x^78+544x^79+1699x^80+872x^81+1853x^82+896x^83+1596x^84+624x^85+1303x^86+344x^87+864x^88+140x^89+635x^90+56x^91+334x^92+16x^93+222x^94+86x^96+51x^98+8x^100+6x^102+5x^104+2x^106+1x^108+1x^110 The gray image is a linear code over GF(2) with n=328, k=14 and d=140. This code was found by Heurico 1.16 in 34.5 seconds.