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

generates a code of length 98 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 97.

Homogenous weight enumerator: w(x)=1x^0+64x^97+142x^98+16x^99+13x^100+8x^101+2x^102+8x^105+1x^112+1x^116

The gray image is a code over GF(2) with n=784, k=8 and d=388.
This code was found by Heurico 1.16 in 6.72 seconds.