The generator matrix

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

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+74x^79+146x^80+296x^81+395x^82+502x^83+696x^84+816x^85+970x^86+1180x^87+1279x^88+1278x^89+1338x^90+1366x^91+1246x^92+1090x^93+988x^94+730x^95+570x^96+462x^97+333x^98+192x^99+113x^100+110x^101+56x^102+38x^103+31x^104+36x^105+14x^106+12x^107+6x^108+8x^109+2x^110+2x^111+5x^112+3x^116

The gray image is a linear code over GF(2) with n=360, k=14 and d=158.
This code was found by Heurico 1.16 in 47 seconds.