The generator matrix

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

generates a code of length 96 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+258x^89+1043x^90+1514x^91+2529x^92+2794x^93+3614x^94+3458x^95+3841x^96+3152x^97+2930x^98+2304x^99+2146x^100+1306x^101+825x^102+406x^103+333x^104+114x^105+82x^106+14x^107+44x^108+16x^109+17x^110+12x^111+1x^112+8x^113+1x^114+4x^115+1x^116

The gray image is a code over GF(2) with n=768, k=15 and d=356.
This code was found by Heurico 1.16 in 17.1 seconds.