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

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 102.

Homogenous weight enumerator: w(x)=1x^0+1x^102+10x^103+1x^104+2x^105+1x^106

The gray image is a linear code over GF(2) with n=388, k=4 and d=204.
This code was found by Heurico 1.16 in 0.534 seconds.