The generator matrix

 1  0  0  0  0  1  1  1  1  1  1  1  X X^2  1  1  1  1 X^2+X  X X^2+X  1 X^2+X  1  X X^2+X X^2  1  X  1 X^2  1  1 X^2  1  1  1  1  1  1 X^2+X  X X^2+X  1  1 X^2  X  X  1  1 X^2+X  1 X^2  X  X  1  1  1  1  0  X X^2  1  1  1  1  1  1  1  X  X  1  1  1 X^2+X  X X^2 X^2+X  1  1
 0  1  0  0  0  0 X^2 X^2  0 X^2+1 X^2+X+1 X+1  1  1 X^2+X X^2+1 X^2+X+1 X+1 X^2 X^2+X  1  0  X X^2  1  1 X^2+X X^2+1  1 X+1  1 X^2+X X+1 X^2 X^2+X  0  X  1  0 X^2+1 X^2 X^2+X  1 X^2+1  0  X  1 X^2  1  1 X^2+X X^2+1  1 X^2+X  1 X^2 X^2+X  0  1  1 X^2+X  1 X^2+X+1 X^2+X+1 X^2+X+1  X X^2+X X^2  0  1  1  0  0 X^2+X+1 X^2  X  1  X X^2+1 X^2
 0  0  1  0  0  0 X^2+1 X+1  1  1 X^2 X^2+X+1  0 X^2+X+1  X  X X^2+X+1  X  1  1 X^2+X+1  X  X X^2+X+1 X^2+1 X^2+X  1  1  1  X X^2 X+1 X^2  X  1 X^2  0 X^2 X^2 X^2+X+1  1  1 X^2+1 X^2+X X^2+1  1  1  1 X^2+X X^2+X+1  X X+1 X+1  X X^2+X  1  0  1 X+1 X^2+X  1 X+1 X^2 X^2+1 X+1 X+1  X X^2+X+1 X+1 X^2+1  0  X X^2+X  X  X  1  1  1 X+1  0
 0  0  0  1  0  1  1  X  X X^2+X X^2+X X^2+1 X^2+1 X^2+X+1  1 X^2+X+1 X^2+X+1 X^2  1  X X^2  0  1 X+1  0  X X^2+1  0 X+1  1 X+1  1 X^2  1 X+1  X  X X^2 X^2+1 X^2+1  X X^2+X+1 X+1  1  0  1  1 X+1 X^2+X+1  X  X  X  X X^2 X^2+X+1  0  0 X^2 X^2 X^2+X  X  1 X^2+X+1  X  0 X^2+X+1 X+1 X^2  1 X+1 X^2 X^2+X+1 X^2+X+1  0  1 X^2+X X^2 X^2+1 X^2+X+1 X^2
 0  0  0  0  1  1 X^2  0 X+1 X^2  0  1 X^2+X+1 X+1 X^2+X X^2+X+1 X^2 X+1 X^2+X X^2+1 X^2+X X^2+1  1  1  1 X^2+X+1  1 X+1 X^2+X X^2 X^2+X X+1 X^2 X^2+X+1  0  0 X^2+1 X^2+1  1  0 X^2+1  1 X+1 X+1 X^2+X X^2+X X^2 X^2+1  X X+1  1 X^2+X  1  1  1  0  1 X+1  0 X^2  X X^2+1 X+1 X^2 X^2+X+1 X+1 X+1 X^2+1 X^2+1 X^2+X+1 X^2+X+1 X^2+X  0 X^2  0 X^2 X^2+X  0 X^2+X X^2
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  X  X X^2+X X^2+X  X X^2+X X^2+X  X X^2+X  X X^2+X  X  X  X  X X^2+X X^2+X X^2+X  X X^2+X  X  X X^2+X X^2+X  X X^2  X X^2+X X^2+X X^2  X X^2+X  0  0  X X^2  0 X^2  X X^2+X X^2+X

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+140x^68+552x^69+1114x^70+1872x^71+2684x^72+3892x^73+4852x^74+6466x^75+7463x^76+9374x^77+9663x^78+11648x^79+11124x^80+11238x^81+10268x^82+10014x^83+7893x^84+6668x^85+4804x^86+3610x^87+2164x^88+1462x^89+858x^90+584x^91+342x^92+148x^93+87x^94+46x^95+26x^96+8x^97+2x^98+2x^100+2x^101+1x^104

The gray image is a linear code over GF(2) with n=320, k=17 and d=136.
This code was found by Heurico 1.13 in 262 seconds.