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 X^2  1  0  0  X  0  1  1  X  1 X^2  X  0  1 X^2  X  1 X^2  X X^2  0  1  1  1 X^2  1 X^2  1 X^2  X X^2  1  1  X  X X^2  X  1  1  1 X^2  X X^2  1  1 X^2  1  1
 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 X^2  X X^2+X  X  X  X X^2+X  X  X  X  X  0  0 X^2  0 X^2 X^2+X  X X^2  0  0 X^2 X^2  X X^2  X X^2  X  0  X  X X^2  0  X X^2+X  X X^2 X^2  0  0  0 X^2+X X^2+X X^2+X  X X^2 X^2 X^2 X^2+X  X X^2 X^2 X^2
 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 X^2 X^2+X  0  X  0  X X^2+X X^2 X^2+X  X X^2+X  X X^2+X X^2+X X^2+X  X X^2  0  X  X  X  0  X X^2  X  X X^2+X  0  0 X^2 X^2  X  X  X X^2  X  X  X X^2+X X^2  X  0 X^2  0  0  X  0 X^2 X^2+X X^2  X X^2+X  0
 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  0  X X^2  0 X^2+X X^2 X^2  0  0  X X^2  X X^2+X  X X^2+X X^2  X X^2  0 X^2  0 X^2+X  X  X X^2+X  X X^2+X  X X^2+X  0 X^2+X X^2+X X^2  0  0 X^2 X^2 X^2+X X^2+X X^2+X X^2+X  X X^2+X  X X^2  0  0 X^2+X  X X^2  0 X^2+X  0  X
 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 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  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 X^2 X^2 X^2 X^2  0
 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  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0
 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 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2  0 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  0  0  0 X^2  0 X^2 X^2 X^2  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  0 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  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2
 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  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  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+80x^78+88x^79+192x^80+288x^81+347x^82+394x^83+475x^84+636x^85+867x^86+872x^87+884x^88+1166x^89+1360x^90+1422x^91+1063x^92+1142x^93+1202x^94+856x^95+597x^96+566x^97+530x^98+342x^99+265x^100+216x^101+157x^102+104x^103+84x^104+74x^105+48x^106+18x^107+21x^108+6x^109+13x^110+2x^112+2x^113+3x^114+1x^126

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 32.6 seconds.