The generator matrix

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

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+74x^96+128x^97+32x^98+16x^100+4x^112+1x^128

The gray image is a linear code over GF(2) with n=388, k=8 and d=192.
This code was found by Heurico 1.16 in 0.541 seconds.