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  2  X  0  X  2  X 2X  X  X  X 2X+2  X  X  X  X  1 2X 2X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X 2X+2  X  X  X  X  X  0  2 2X+2 2X+2 2X+2 2X+2 2X+2  0 2X 2X  X  X  X  X 2X+2  2 2X+2 2X+2  1  1
 0  X  2 3X+2  0 3X+2  2 3X 2X X+2 2X+2 3X 2X X+2 2X+2  X  0 3X+2  2 3X  0 3X+2  2 3X 2X X+2 2X+2  X 2X X+2 2X+2  X 3X+2  X 3X  X 3X+2  X 3X  X X+2  X  0  2  X  X 2X 2X+2 X+2  X  0  X  X  2 3X+2 3X  0  2 3X+2 3X 2X 2X+2 2X 2X+2 X+2  X X+2  X  0  2 2X 2X+2  2 3X+2 3X X+2  X  0  X  X  0 2X+2 2X 2X+2  2  X  X  X X+2 3X 3X+2  X 2X  X  X  X  0  2
 0  0 2X 2X 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0 2X  0  0 2X 2X  0 2X 2X  0 2X 2X 2X  0 2X  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0  0  0  0  0  0 2X  0 2X 2X  0 2X  0 2X 2X  0 2X 2X  0 2X 2X  0  0  0 2X 2X  0  0 2X  0  0  0

generates a code of length 98 over Z4[X]/(X^2+2X+2) 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 6.52 seconds.