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

generates a code of length 98 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+380x^96+512x^98+128x^104+3x^128

The gray image is a code over GF(2) with n=784, k=10 and d=384.
This code was found by Heurico 1.16 in 1.61 seconds.