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

generates a code of length 94 over Z2[X]/(X^3) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+58x^83+134x^84+178x^85+268x^86+266x^87+367x^88+416x^89+464x^90+586x^91+512x^92+648x^93+640x^94+616x^95+639x^96+498x^97+374x^98+346x^99+307x^100+176x^101+184x^102+122x^103+82x^104+92x^105+65x^106+42x^107+23x^108+28x^109+16x^110+12x^111+15x^112+10x^113+4x^114+2x^117+1x^138

The gray image is a linear code over GF(2) with n=376, k=13 and d=166.
This code was found by Heurico 1.16 in 9.4 seconds.