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

generates a code of length 98 over Z2[X]/(X^3) who�s minimum homogenous weight is 97.

Homogenous weight enumerator: w(x)=1x^0+66x^97+20x^98+14x^99+6x^100+6x^101+4x^102+2x^103+8x^105+1x^136

The gray image is a linear code over GF(2) with n=392, k=7 and d=194.
This code was found by Heurico 1.16 in 0.907 seconds.