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

generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+60x^70+80x^71+172x^72+214x^73+341x^74+406x^75+434x^76+560x^77+765x^78+932x^79+1100x^80+1280x^81+1201x^82+1368x^83+1324x^84+1254x^85+1129x^86+890x^87+716x^88+550x^89+400x^90+294x^91+239x^92+180x^93+153x^94+96x^95+95x^96+52x^97+41x^98+28x^99+10x^100+6x^101+4x^102+2x^103+4x^104+1x^106+1x^108+1x^118

The gray image is a linear code over GF(2) with n=332, k=14 and d=140.
This code was found by Heurico 1.16 in 28.6 seconds.