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

generates a code of length 96 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+114x^92+232x^94+364x^96+208x^98+70x^100+8x^102+24x^104+2x^120+1x^128

The gray image is a code over GF(2) with n=768, k=10 and d=368.
This code was found by Heurico 1.16 in 1.11 seconds.