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

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+66x^97+146x^98+14x^99+6x^100+6x^101+4x^102+2x^103+1x^104+8x^105+2x^114

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 47.9 seconds.