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

generates a code of length 97 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+13x^96+222x^97+14x^98+2x^112+2x^113+2x^114

The gray image is a code over GF(2) with n=776, k=8 and d=384.
This code was found by Heurico 1.16 in 0.828 seconds.