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 X X X X X X X X 1 1 1 X X 1 X X 1 X X X X X X X X X X X X X X X X X X 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
0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 2X 2 2X 2 2X 2 2X 2 2X 2 2X 2 2X 2 2X 2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 0 0 0 2X 0 0 2X 0 0 2X 2X 0 0 2 2 2 2 2X 2X 0 2X 0 2 2 2 2 0 2X+2 2 2X 2X+2 2 2X 2X 2X 2X 2X+2 2 2X+2 2 2X+2 2 0 2X 2X+2 2 0 2X 2X+2 2 0 2X 0 2X 2X+2 2
0 0 2X 0 0 0 2X 0 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 2X 2X 2X 0 0 0 0 0 2X 2X 2X 2X 2X 0 0 2X 2X 0 2X 0 2X 2X 2X 0 0 2X 0 2X 0 2X 0 0 0 0 0 2X 2X 0 0 0 0 2X 2X 0 0 2X 2X 2X 2X 0 0 2X 2X 2X 2X 0 0 2X 2X
0 0 0 2X 0 0 0 2X 2X 2X 2X 2X 2X 0 2X 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 0 0 2X 0 2X 2X 0 2X 0 0 2X 2X 0 2X 2X 0 2X 0 0 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0
0 0 0 0 2X 2X 2X 2X 2X 0 0 2X 0 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 0 2X 2X 2X 0 2X 2X 0 0 2X 2X 0 2X 0 0 2X 2X 2X 0 0 2X 2X 0 0 2X 2X 2X 2X 0 2X 0 2X 2X 2X 2X 0 0 2X 2X 0 0 0 0 2X 2X 0 0 0 0 0 0
generates a code of length 96 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 96.
Homogenous weight enumerator: w(x)=1x^0+508x^96+3x^128
The gray image is a code over GF(2) with n=768, k=9 and d=384.
This code was found by Heurico 1.16 in 1.08 seconds.