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

generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+58x^78+120x^79+145x^80+272x^81+330x^82+362x^83+555x^84+580x^85+710x^86+918x^87+1099x^88+1138x^89+1313x^90+1402x^91+1238x^92+1300x^93+1032x^94+880x^95+657x^96+492x^97+440x^98+318x^99+284x^100+192x^101+160x^102+128x^103+100x^104+42x^105+48x^106+28x^107+15x^108+16x^109+3x^110+2x^111+2x^112+1x^114+2x^115+1x^134

The gray image is a linear code over GF(2) with n=364, k=14 and d=156.
This code was found by Heurico 1.16 in 31.8 seconds.