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

generates a code of length 98 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+286x^96+128x^97+256x^98+128x^99+192x^100+31x^104+1x^112+1x^184

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 12.9 seconds.