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 X^2  X  0  X  0  X  0  1  X  X  0  X  1  0  1  X  X  1  1  1  1  1  1  X  1  X  X  1  0  0  1  1  1  1  0  0  1  1 X^2  1  X  X  1  1  1  1  1  X
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X X^2+X  0 X^2+X  X X^2 X^2+X X^2+X  0  0  X X^2+X X^2 X^2  0  0 X^2+X  X X^2+X  0  0  0 X^2  0  X X^2+X X^2  X  X X^2+X  X  X X^2+X X^2  X  X  X  X X^2  X  0  X  X X^2  0  0 X^2  X X^2+X  0 X^2+X  X X^2+X X^2+X  X X^2  0  X X^2  X  0 X^2 X^2  X  0 X^2  0 X^2+X  X  X X^2+X  X X^2 X^2+X X^2+X X^2 X^2+X X^2  X X^2+X  0  0
 0  0  X  0  X  X X^2+X  0  0  0  X X^2  X X^2+X X^2 X^2+X X^2 X^2 X^2  0  X  X X^2+X  X  X  X X^2+X X^2 X^2  X X^2 X^2+X  0 X^2 X^2 X^2  X X^2  X X^2+X  0  X  0 X^2+X  0  X  X X^2+X X^2  X X^2 X^2  0 X^2 X^2+X  X  0 X^2+X X^2+X  X  X  0  0  X X^2+X  X X^2+X X^2+X X^2+X  X  X  0 X^2+X  X  X X^2  X  X  X X^2 X^2+X X^2 X^2+X  X  X  0 X^2+X  X X^2+X X^2+X  0  0 X^2
 0  0  0  X  X  0 X^2+X  X  0  X  0  X X^2+X X^2+X X^2 X^2  0 X^2  X X^2+X  0  0 X^2+X  X  0  0  X X^2+X  0  X  X  X  0 X^2  0 X^2+X X^2  X  0 X^2  0 X^2+X X^2  0 X^2+X  0 X^2 X^2+X X^2+X X^2  X  X  0  X  X X^2 X^2+X  X  X  X X^2+X  X  0  X X^2+X X^2  X X^2 X^2 X^2 X^2 X^2+X  0  0 X^2  0 X^2 X^2+X  0 X^2  X X^2 X^2+X  0 X^2+X X^2 X^2 X^2+X  0 X^2+X  X X^2 X^2
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0  0  0  0 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 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 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2 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  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 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 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2
 0  0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 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  0  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0
 0  0  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  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  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+138x^80+326x^82+12x^83+660x^84+52x^85+792x^86+180x^87+1315x^88+448x^89+1394x^90+840x^91+1628x^92+1032x^93+1626x^94+824x^95+1423x^96+480x^97+1094x^98+172x^99+759x^100+36x^101+484x^102+20x^103+346x^104+142x^106+98x^108+26x^110+24x^112+4x^114+7x^116+1x^136

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 35.1 seconds.