The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+78x^87+896x^88+2306x^89+4103x^90+5600x^91+8400x^92+10736x^93+12664x^94+13804x^95+14522x^96+13794x^97+13222x^98+10212x^99+7961x^100+5534x^101+3414x^102+1822x^103+1039x^104+494x^105+217x^106+96x^107+91x^108+30x^109+10x^110+2x^111+18x^112+2x^113+2x^114+2x^119

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 236 seconds.