The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1 X^2+X  1  1  1  0  1  1 X^2+X  X  1  1  1  1  0  1  1  0  1  1 X^2+X  1  1  1  1  0 X^2+X  1 X^2+X  1  1  1  0  1 X^2  1  0  1  1  1  1  1  1  1  1  1 X^2+X X^2  X  1 X^2+X X^2 X^2+X  1  1  1  1  0  1  X X^2  1  1  0  X  1  1  0  1  1  0  1  1  1  1  1  1  0 X^2+X X^2+X  1  1  X  X  1 X^2  X
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X  1 X^2+1  0 X+1  1 X^2+X X^2+1  1  1 X^2+X+1  0 X^2+1 X^2+X  1 X^2 X^2+1  1 X^2+X X^2+1  1 X+1 X+1 X+1 X^2+X  1  1  0  1  X  0 X^2  1 X^2  1 X^2+X  1 X^2+1 X^2+X X+1 X+1  X X^2+1 X^2+X+1  1 X^2+1  1  1  1 X^2+X+1  1  1  1 X^2+X+1  1 X+1 X^2+X+1  1  X  1  1 X^2 X+1  1  1 X^2+1 X+1  1 X^2+X  0  1 X^2+X X^2+X  0  X  0  0  1  1  1 X^2+1 X+1 X^2  1  0  1 X^2+X
 0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2
 0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  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  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0  0  0  0
 0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 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 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0
 0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  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+294x^88+252x^90+677x^92+508x^94+687x^96+468x^98+683x^100+308x^102+177x^104+11x^108+13x^112+5x^116+9x^120+3x^128

The gray image is a linear code over GF(2) with n=384, k=12 and d=176.
This code was found by Heurico 1.16 in 63.5 seconds.