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  X  X  X  0  1  0  1  1  X X^2  X  1  1 X^2  X  1  0  1  X  X  0  1  1  1  X  1  1  1 X^2  1  0  1  1  0  1 X^2  1  1  0  0  1  X X^2 X^2  1  1  X  X  X X^2  1  X  X  1  X
 0  X  0  X  0  0  X X^2+X  0  0  X X^2+X X^2  0 X^2+X X^2 X^2+X X^2  X X^2+X  X X^2  0 X^2+X X^2+X  0  X X^2 X^2+X  X  0  0  0 X^2+X X^2+X X^2+X X^2+X X^2 X^2 X^2 X^2+X  X  0 X^2  0 X^2+X  X  X  X X^2+X  X  X  0 X^2+X  X X^2  X  0 X^2  0  0 X^2 X^2+X  X  X  X  X  X X^2  0  X  X  X  0  0 X^2 X^2  0 X^2  X  0  X X^2+X X^2  X  X X^2+X  X  0 X^2+X X^2  0  X
 0  0  X  X  0 X^2+X  X  0  0 X^2+X  X  0  X X^2  X X^2  0 X^2+X  X  0 X^2+X  X  0  X X^2  0 X^2  X  X  0  0 X^2+X X^2+X X^2+X X^2 X^2  X  X  X  X  0 X^2  0  X X^2+X  X X^2+X X^2+X X^2+X X^2+X X^2  X X^2+X X^2  0  0  X X^2+X  X X^2 X^2 X^2  0  0 X^2+X  0 X^2+X X^2+X  X X^2+X X^2+X  0  X  X X^2 X^2+X  X  X  X  0  X  X  0  X X^2  X X^2+X X^2+X X^2 X^2  X X^2  X
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  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 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2
 0  0  0  0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0  0
 0  0  0  0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0  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+187x^80+4x^81+260x^82+56x^83+766x^84+120x^85+776x^86+244x^87+1173x^88+524x^89+1310x^90+692x^91+1770x^92+736x^93+1548x^94+760x^95+1514x^96+556x^97+1124x^98+272x^99+795x^100+104x^101+496x^102+20x^103+277x^104+4x^105+102x^106+4x^107+125x^108+12x^110+30x^112+4x^114+15x^116+2x^120+1x^124

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 36.1 seconds.