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 X X X X X X X X X X X X X X X 2 X X X X X 2 X 2 X X 2 2 2 X 2X 2X
0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 2X 2X 0 0 2X 2X 0 0 0 2X 0 2X 0 2X 2X 2X 0 2X 2X 0 2X 0 0 2X 2X 0 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 2X 2X 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 0 0 2X 2X 0 2X 0 2X 2X 0 0 2X 2X 2X 2X 2X 2X 0 0 2X 2X 2X 0 2X 2X 0
0 0 0 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 2X 0 0 2X 2X 2X 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 2X 2X 0 0 0 2X 0 0 2X 2X 0 2X 2X 2X 0
0 0 0 0 2X 0 0 0 2X 2X 2X 2X 2X 0 2X 2X 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 2X 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 0 0 0 2X 2X 2X 2X 2X 2X 0 2X 0 0 2X 2X 2X 0 2X 0 0 0 0 2X 0 0 0 0 0
0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X 2X 2X 0 0 0 0 2X 0 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 2X 2X 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 0 0 0 0 0 2X 2X 0 2X 2X 2X 2X 0 0 2X 2X 2X 0 0 0 2X 2X 0 2X 0 0 2X 2X
0 0 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 2X 0 2X 2X 2X 0 0 2X 0 2X 2X 0 0 2X 2X 0 2X 2X 0 2X 0 0 2X 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 0 2X 2X 2X 2X 0 0 0 2X 0 2X 0 2X 2X
generates a code of length 96 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 92.
Homogenous weight enumerator: w(x)=1x^0+168x^92+128x^94+464x^96+128x^98+106x^100+12x^104+12x^108+2x^112+2x^116+1x^128
The gray image is a code over GF(2) with n=768, k=10 and d=368.
This code was found by Heurico 1.16 in 68 seconds.