The generator matrix

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

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+160x^70+660x^71+1059x^72+1938x^73+2779x^74+4112x^75+4754x^76+6422x^77+7501x^78+9414x^79+9818x^80+11184x^81+11033x^82+11258x^83+10211x^84+9468x^85+7795x^86+6914x^87+4752x^88+3714x^89+2296x^90+1658x^91+913x^92+626x^93+274x^94+148x^95+102x^96+52x^97+32x^98+12x^99+6x^100+4x^101+2x^102

The gray image is a linear code over GF(2) with n=328, k=17 and d=140.
This code was found by Heurico 1.13 in 269 seconds.