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  0  X  X  X  X  1 X^2  X X^2  0  X  0 X^2  1  X  X  1 X^2 X^2  1  1 X^2  X  1  1  1  1  0  1  1  1 X^2  X  1  X X^2  X  X X^2 X^2  X  1  X  X  1 X^2  0  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^2+X X^2  X  0 X^2+X X^2 X^2  0 X^2 X^2+X X^2+X  X X^2  0  0  X X^2 X^2+X X^2+X  0  0 X^2 X^2 X^2+X  X  0  X X^2 X^2  0 X^2+X X^2  X X^2  X X^2  0  X X^2  X  X  X  0  X  X X^2+X X^2  0 X^2+X X^2 X^2+X X^2 X^2 X^2 X^2  X X^2 X^2  0  X  X  X  X X^2+X  X  X  X X^2+X
 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 X^2+X X^2+X  0  X  X X^2 X^2  X X^2+X X^2+X X^2  0  X X^2 X^2  0  X  X  0  0  0  X  X  X  0 X^2 X^2  X X^2  X X^2+X  X X^2 X^2+X X^2  0 X^2+X  0  0 X^2 X^2+X  X  X  X X^2  0 X^2+X  X  X  X  0  0 X^2 X^2+X  X  0 X^2  0  X  0  0  X  0  X
 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 X^2+X X^2  0  0 X^2 X^2 X^2 X^2+X X^2+X X^2  0 X^2+X  0  X X^2+X  0 X^2 X^2+X X^2  0 X^2 X^2  0 X^2  0  0 X^2+X  X  X  X X^2+X X^2 X^2+X  0 X^2+X X^2+X  X  0  X  X X^2 X^2+X X^2  X  0  0 X^2 X^2  0 X^2+X  0  X  X  X X^2  0 X^2+X  X X^2+X X^2+X X^2  X  X  0  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 X^2 X^2 X^2  X  X  0  0 X^2+X X^2+X  X X^2+X X^2  0 X^2+X X^2 X^2  0 X^2+X  X X^2 X^2  X X^2  X X^2+X  X X^2+X  X  0  X  X  0  0  X X^2+X  0  0  0 X^2 X^2  X X^2+X X^2 X^2+X X^2  X X^2  0 X^2  X  X  X X^2+X  X X^2  X  0  X  0 X^2 X^2+X X^2+X  X  0  0  0  X
 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 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0  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 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  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  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2  0 X^2  0  0  0  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2  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+66x^80+102x^81+201x^82+304x^83+341x^84+448x^85+513x^86+698x^87+860x^88+936x^89+992x^90+962x^91+1208x^92+1376x^93+1156x^94+1052x^95+976x^96+874x^97+800x^98+536x^99+421x^100+464x^101+309x^102+214x^103+162x^104+116x^105+101x^106+70x^107+46x^108+32x^109+22x^110+4x^111+15x^112+4x^113+1x^114+1x^122

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 34.4 seconds.