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

generates a code of length 94 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+75x^86+8x^87+176x^88+36x^89+204x^90+76x^91+260x^92+136x^93+279x^94+144x^95+181x^96+68x^97+120x^98+28x^99+82x^100+16x^101+54x^102+47x^104+24x^106+18x^108+7x^110+2x^112+4x^114+1x^118+1x^152

The gray image is a linear code over GF(2) with n=376, k=11 and d=172.
This code was found by Heurico 1.16 in 1.09 seconds.