The generator matrix

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

generates a code of length 96 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+90x^88+1034x^89+2086x^90+3144x^91+4586x^92+5318x^93+6571x^94+7286x^95+7144x^96+6470x^97+6297x^98+4888x^99+3950x^100+2810x^101+1713x^102+1066x^103+564x^104+280x^105+98x^106+72x^107+40x^108+8x^109+10x^110+4x^111+1x^112+1x^114+4x^115

The gray image is a code over GF(2) with n=768, k=16 and d=352.
This code was found by Heurico 1.16 in 61.9 seconds.