The generator matrix

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

generates a code of length 96 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+124x^87+904x^88+2382x^89+3938x^90+6160x^91+8044x^92+10056x^93+12760x^94+13874x^95+14796x^96+14102x^97+12776x^98+10564x^99+7974x^100+5482x^101+3243x^102+1904x^103+1011x^104+504x^105+260x^106+68x^107+68x^108+46x^109+15x^110+10x^111+2x^112+4x^113

The gray image is a code over GF(2) with n=768, k=17 and d=348.
This code was found by Heurico 1.16 in 222 seconds.