The generator matrix

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

generates a code of length 96 over Z4[X]/(X^3+2,2X) 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.