The generator matrix

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

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+79x^88+309x^90+578x^92+572x^94+533x^96+625x^98+551x^100+423x^102+259x^104+84x^106+33x^108+26x^110+6x^112+5x^114+5x^116+3x^118+1x^120+1x^122+1x^124+1x^136

The gray image is a linear code over GF(2) with n=388, k=12 and d=176.
This code was found by Heurico 1.16 in 2 seconds.