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^2  1  1  1  1  1  1  1  1  X  1  1  1  1  1  X  1  1  1  X  1  1  1  1  1 X^2 X^2  1  1  1  1  0  1 X^2  1  1  0  1 X^2  0 X^2  X  1  0  1  X  1  1  1  1
 0  X  0  0  0  X X^2+X  X X^2  0 X^2+X X^2+X X^2 X^2 X^2+X X^2+X X^2  0 X^2+X X^2+X  0  X X^2 X^2+X  0 X^2+X  0  0 X^2  X  X X^2+X  0 X^2  X X^2  0  X X^2+X X^2+X X^2+X X^2  0  X  0  0 X^2 X^2+X  0 X^2+X  0  0  X X^2+X X^2 X^2  0 X^2+X  0 X^2+X  X X^2+X  0 X^2+X  X  0 X^2 X^2  X X^2+X X^2+X  X X^2  X X^2  0  0  X  X X^2 X^2+X  0 X^2 X^2  X  0  X X^2 X^2+X  X X^2  0 X^2 X^2 X^2 X^2+X
 0  0  X  0  X  X  X  0 X^2  0 X^2+X X^2  X X^2+X X^2+X X^2  0 X^2+X  X  0  0 X^2 X^2+X  X  0  X  X X^2 X^2+X  X X^2  0  0  0  X  X  X X^2  0 X^2+X  0 X^2 X^2 X^2+X X^2+X X^2+X  X  0  0  0 X^2+X  X X^2+X X^2  0  X X^2+X  0  X X^2 X^2+X  0 X^2  0  X X^2 X^2  X  0 X^2+X X^2 X^2+X  X  X  X  X X^2+X  X X^2  X X^2+X X^2+X  X  X X^2  0 X^2+X X^2+X  X X^2 X^2+X  X  X X^2 X^2+X  0
 0  0  0  X  X  0  X X^2+X  0 X^2+X  X X^2  0  X  0 X^2+X  X X^2 X^2+X X^2  0 X^2+X X^2+X X^2  0 X^2 X^2 X^2+X X^2+X X^2+X X^2+X  0 X^2  X X^2  0 X^2+X X^2+X  0 X^2+X  0  X  0 X^2  0 X^2+X  X  X X^2 X^2+X  X  0  X X^2 X^2+X  0  0  0 X^2+X  X  0 X^2 X^2  X X^2+X  X  X X^2  X  0  X  0  X X^2  0 X^2 X^2+X X^2+X  0  0  0 X^2  X X^2  X  X X^2+X X^2  X X^2+X X^2+X  X X^2+X X^2  X X^2+X
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2
 0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  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+24x^88+108x^89+108x^90+44x^91+197x^92+102x^93+285x^94+36x^95+390x^96+54x^97+250x^98+24x^99+156x^100+52x^101+38x^102+20x^103+48x^104+36x^105+8x^106+4x^107+15x^108+30x^109+11x^110+1x^112+2x^113+1x^114+2x^118+1x^162

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 1.16 seconds.