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

generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+39x^82+34x^83+87x^84+54x^85+98x^86+96x^87+122x^88+192x^89+191x^90+276x^91+194x^92+204x^93+99x^94+80x^95+84x^96+48x^97+48x^98+26x^99+9x^100+14x^101+24x^102+6x^104+9x^106+6x^108+2x^110+3x^112+1x^114+1x^158

The gray image is a linear code over GF(2) with n=364, k=11 and d=164.
This code was found by Heurico 1.16 in 1.09 seconds.