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

generates a code of length 92 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+261x^80+36x^81+462x^82+112x^83+665x^84+392x^85+712x^86+788x^87+914x^88+1260x^89+742x^90+1520x^91+937x^92+1496x^93+784x^94+1272x^95+701x^96+772x^97+646x^98+384x^99+561x^100+128x^101+332x^102+20x^103+231x^104+12x^105+134x^106+67x^108+28x^110+11x^112+2x^116+1x^120

The gray image is a linear code over GF(2) with n=368, k=14 and d=160.
This code was found by Heurico 1.16 in 49.4 seconds.