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  1  1  1  X  X  X  1  1  1  X  X  X  1  1  1  X  X  X  1  1  1  X  2  2  2  X  X  X  X  1  1  2  2  2  X  1  1  X  X  X 2X 2X 2X 2X  0  0  0  X  2  X  2  2  2  2  1  X  1  0 2X  0 2X  2
 0 2X  0 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X  0 2X 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X 2X  0 2X 2X  0  0  0 2X 2X  0  0  0  0 2X 2X 2X  0  0
 0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X  0 2X  0 2X  0 2X  0 2X 2X  0 2X 2X  0  0  0  0 2X  0 2X  0  0  0 2X  0 2X 2X  0  0

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

Homogenous weight enumerator: w(x)=1x^0+54x^98+2x^100+6x^102+1x^104

The gray image is a code over GF(2) with n=776, k=6 and d=392.
This code was found by Heurico 1.16 in 2.41 seconds.