The generator matrix

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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+180x^72+728x^73+1177x^74+2020x^75+2713x^76+4018x^77+4969x^78+6762x^79+7651x^80+8968x^81+9651x^82+10902x^83+10774x^84+11248x^85+9896x^86+9814x^87+7607x^88+6902x^89+5045x^90+3858x^91+2320x^92+1494x^93+997x^94+636x^95+377x^96+156x^97+99x^98+52x^99+25x^100+16x^101+6x^102+4x^103+6x^105

The gray image is a linear code over GF(2) with n=336, k=17 and d=144.
This code was found by Heurico 1.13 in 278 seconds.