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  X  X  1  1  1  X  X  X  1  1  1  X  X  X  1  1  1  X  X  X  1  1  1  X X^2 X^2 X^2  X  X  X  X  1  1 X^2 X^2 X^2  X  1  1  X  X  X X^3 X^3 X^3 X^3  0  0  0  X X^2  X X^2 X^2 X^2 X^2  1  X  1  0 X^3  0 X^3 X^2
 0 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0  0
 0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3  0  0

generates a code of length 97 over Z2[X]/(X^4) who´s minimum homogenous weight is 98.

Homogenous weight enumerator: w(x)=1x^0+54x^98+2x^100+6x^102+1x^104

The gray image is a linear code over GF(2) with n=776, k=6 and d=392.
This code was found by Heurico 1.16 in 2.3 seconds.