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  2  1
 0  X  0  X  2  2 X+2 X+2 X^2 X^2+X X^2 X^2+X X^2+2 X^2+X+2 X^2+2 X^2+X+2  0  X X^2 X+2 X^2+2 X+2 X^2+X X^2  0 X^2+X+2 X+2 X^2  0  0 X^2+X X^2+X+2 X^2+2 X^2+X  2 X+2 X^2+X  0  X X^2+2 X^2+X+2 X+2 X^2+2  2 X+2  0 X^2+X X^2+2 X^2+X X^2+2 X^2 X^2+X+2 X^2+X+2 X^2  2 X^2+X X+2 X^2+2  2  X X+2  2  2 X+2  X  0 X^2+X+2 X^2+2 X^2+X  0  0 X^2+X X^2  X X^2+X+2 X^2 X^2  2 X^2 X+2 X^2+X  X X^2  X X^2+X+2 X^2 X^2+X+2  X  2  X  0 X^2+X+2  2  2  X X^2
 0  0  X  X X^2 X^2+X+2 X^2+X X^2+2 X^2 X^2+X  X  0  0  X X^2+X+2 X^2+2  0  X  X X^2+2  0 X^2+X X^2+2 X^2+X X^2+X+2 X+2  2 X^2+2 X^2 X+2 X^2+X+2  0 X^2+2  2 X+2  X X^2+2 X^2+X X^2+X+2  2 X^2+X X^2 X+2 X^2+2  0  2 X+2 X^2+X+2  X X^2+2 X^2+X+2 X^2 X^2+X+2  2 X+2  0  X  X X^2+X+2 X^2+X+2 X^2  2 X^2+2  2 X^2 X^2+2  0 X^2 X^2+X X^2+X X^2+X+2 X^2+X+2  0  2 X^2+2 X+2 X^2+X  X  2 X^2+X+2  X  0 X^2 X^2+X X^2 X^2+X+2 X+2 X^2 X^2 X+2 X^2+2 X^2+X+2  X X^2+X X^2+2  2
 0  0  0  2  2  2  0  2  0  2  2  2  2  0  0  0  2  0  0  0  0  2  2  2  0  2  2  2  0  2  0  0  2  2  0  0  0  2  2  0  0  0  0  2  2  0  2  2  0  0  0  2  2  2  2  0  2  2  0  0  2  2  0  0  0  2  2  0  0  0  2  2  2  0  2  2  0  2  0  2  2  2  2  0  0  2  0  2  0  2  0  0  0  0  0  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+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 1.17 seconds.