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  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  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  1  1  1  1
 0  X  0 X+2 2X 3X+2 2X 3X  0 3X+2 2X 3X 2X X+2  0  X  0 X+2 2X 3X  0 3X+2 2X  X  0 X+2 2X 3X 2X 3X+2 2X 3X  2 3X 2X+2 X+2 2X+2 X+2  2 3X  X  2  2 3X+2  2 3X 3X+2  2  2 3X 2X+2 X+2  2 X+2 2X+2  X 2X+2 3X  2 X+2 X+2  2 2X+2  X 2X  X 3X 3X+2  2 2X  2 3X+2 2X+2 X+2 2X+2 2X  X X+2  0  2 2X+2  X 3X 3X 3X+2  0  0  2 2X+2 X+2 X+2 3X+2 3X  X X+2 3X+2
 0  0  2  0  0  2 2X+2 2X+2  0  0  0  0 2X+2  2  2 2X+2 2X 2X 2X 2X  2 2X+2 2X+2  2 2X 2X 2X 2X  2 2X+2 2X+2  2 2X+2 2X+2  2  2  0 2X  0  0 2X+2 2X+2 2X+2  2  0 2X  0 2X  0  2  2 2X+2 2X  0 2X+2 2X  2  2  2 2X+2 2X 2X 2X  0  2  0 2X+2  2  2  0  0 2X  0  0  2  2 2X 2X+2  0 2X 2X 2X  0  2  2  2 2X+2  2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2  2  2
 0  0  0  2 2X+2  2 2X+2  0 2X 2X+2  2 2X  2 2X+2 2X 2X 2X  2  2 2X  2 2X+2  0  0 2X+2 2X+2  0  0 2X+2  2 2X 2X 2X+2 2X+2 2X  0  2 2X  0 2X+2  2  2 2X 2X 2X+2 2X+2  0 2X 2X 2X+2 2X+2  0  2 2X  0  2  0  2  2 2X  0 2X+2  0  2  0 2X+2 2X 2X+2 2X+2  0  2  0 2X+2  0  2 2X 2X+2 2X+2  2  0 2X 2X  0  0  0 2X+2 2X+2 2X 2X  2  0 2X+2  2 2X+2 2X  2

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

Homogenous weight enumerator: w(x)=1x^0+168x^92+48x^93+120x^94+208x^95+976x^96+208x^97+96x^98+48x^99+163x^100+8x^102+3x^104+1x^188

The gray image is a code over GF(2) with n=768, k=11 and d=368.
This code was found by Heurico 1.16 in 1.25 seconds.