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

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+102x^88+146x^90+8x^91+234x^92+72x^93+216x^94+176x^95+253x^96+176x^97+208x^98+72x^99+137x^100+8x^101+80x^102+62x^104+38x^106+34x^108+16x^110+6x^112+2x^116+1x^164

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 1.2 seconds.