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

generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+16x^76+28x^77+92x^78+130x^79+212x^80+224x^81+359x^82+366x^83+547x^84+604x^85+749x^86+946x^87+957x^88+1180x^89+1200x^90+1270x^91+1209x^92+1168x^93+978x^94+952x^95+747x^96+602x^97+468x^98+322x^99+281x^100+228x^101+184x^102+98x^103+86x^104+56x^105+46x^106+10x^107+23x^108+4x^109+10x^110+2x^111+12x^112+2x^113+5x^114+4x^116+3x^118+1x^120+2x^122

The gray image is a linear code over GF(2) with n=364, k=14 and d=152.
This code was found by Heurico 1.16 in 33.1 seconds.