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

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

Homogenous weight enumerator: w(x)=1x^0+15x^96+92x^97+14x^98+4x^105+1x^114+1x^146

The gray image is a code over GF(2) with n=388, k=7 and d=192.
This code was found by Heurico 1.16 in 0.717 seconds.