The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X+2  1  2  1  1  1 3X  1 2X  1  1 2X+2  1  1 3X+2  1  1  1 3X  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 X+2  X  2  0  2 3X+2 3X  0 2X 3X+2 X+2 2X+2  2 2X+2  2
 0  1 X+1 3X+2 2X+3  1 X+3  2  1 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  2  1 X+3 3X 2X+1  1 2X  1 X+1 3X+2  1 X+3 2X+3  1 2X+2 3X 2X+1  1 X+2  0  X  2  0 3X+2  2 3X 3X+1  3 3X+3  1 X+1 2X+3 X+1 2X+3 X+3 2X+1 X+3 2X+1 3X+1  3 3X+3  1  0 3X+2  2 X+2 2X 3X 2X+2  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X 2X 2X  0  0 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X  0  0  0  0 2X 2X 2X 2X 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0 2X  0 2X  0 2X 2X  0 2X 2X  0 2X  0
 0  0  0 2X  0 2X 2X 2X 2X  0 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X  0 2X  0  0  0 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0 2X 2X  0 2X  0 2X  0  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X  0  0  0 2X 2X  0 2X  0  0  0 2X 2X 2X  0  0  0  0 2X  0  0
 0  0  0  0 2X  0 2X 2X 2X 2X  0 2X 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0  0  0 2X  0  0 2X 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X 2X 2X  0 2X  0 2X  0  0  0  0  0 2X 2X  0 2X 2X 2X  0 2X 2X  0 2X 2X  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+372x^92+112x^94+1076x^96+112x^98+372x^100+3x^128

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 0.766 seconds.