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

generates a code of length 93 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+52x^80+116x^81+163x^82+272x^83+327x^84+416x^85+561x^86+580x^87+712x^88+884x^89+1026x^90+1206x^91+1306x^92+1398x^93+1311x^94+1150x^95+1009x^96+826x^97+719x^98+596x^99+433x^100+296x^101+251x^102+224x^103+146x^104+124x^105+103x^106+54x^107+38x^108+34x^109+21x^110+14x^111+8x^112+2x^113+4x^114+1x^138

The gray image is a linear code over GF(2) with n=372, k=14 and d=160.
This code was found by Heurico 1.16 in 33.2 seconds.