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

generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+181x^88+28x^90+148x^92+160x^93+140x^94+384x^95+138x^96+320x^97+84x^98+128x^99+88x^100+32x^101+4x^102+151x^104+52x^108+8x^112+1x^176

The gray image is a linear code over GF(2) with n=384, k=11 and d=176.
This code was found by Heurico 1.16 in 1.56 seconds.