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

generates a code of length 93 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+68x^82+122x^83+188x^84+240x^85+275x^86+366x^87+394x^88+492x^89+540x^90+542x^91+625x^92+678x^93+645x^94+604x^95+497x^96+408x^97+375x^98+274x^99+224x^100+150x^101+98x^102+86x^103+72x^104+58x^105+52x^106+46x^107+13x^108+20x^109+22x^110+8x^111+2x^113+4x^114+2x^116+1x^138

The gray image is a linear code over GF(2) with n=372, k=13 and d=164.
This code was found by Heurico 1.16 in 8.85 seconds.