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

generates a code of length 98 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 98.

Homogenous weight enumerator: w(x)=1x^0+34x^98+12x^99+3x^100+6x^102+4x^103+1x^104+3x^108

The gray image is a code over GF(2) with n=784, k=6 and d=392.
This code was found by Heurico 1.16 in 0.719 seconds.