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

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+76x^86+12x^87+186x^88+52x^89+167x^90+144x^91+82x^92+284x^93+102x^94+320x^95+103x^96+172x^97+76x^98+32x^99+62x^100+4x^101+62x^102+4x^103+58x^104+29x^106+16x^108+3x^112+1x^160

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 1.12 seconds.