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

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+116x^92+120x^93+149x^94+256x^95+761x^96+304x^97+130x^98+64x^99+113x^100+24x^101+9x^102+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 1.19 seconds.