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

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

Homogenous weight enumerator: w(x)=1x^0+34x^97+6x^98+8x^99+7x^100+2x^101+4x^103+1x^106+1x^110

The gray image is a linear code over GF(2) with n=388, k=6 and d=194.
This code was found by Heurico 1.16 in 0.715 seconds.