The generator matrix

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

generates a code of length 96 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+230x^90+868x^91+1407x^92+1700x^93+1934x^94+2024x^95+1634x^96+1484x^97+1356x^98+1160x^99+772x^100+684x^101+442x^102+276x^103+221x^104+112x^105+42x^106+8x^107+17x^108+4x^109+4x^110+2x^112+2x^116

The gray image is a code over GF(2) with n=768, k=14 and d=360.
This code was found by Heurico 1.16 in 5.31 seconds.