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

generates a code of length 98 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 98.

Homogenous weight enumerator: w(x)=1x^0+106x^98+4x^100+12x^102+2x^104+2x^106+1x^112

The gray image is a code over GF(2) with n=784, k=7 and d=392.
This code was found by Heurico 1.16 in 1.59 seconds.