The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1 2X+2  1  X  1  1  X  1  2 2X+2  1  X  1  1  X  0  1 2X+2  1  X  2 2X+2 2X+2  0  1  X  1
 0  X  0  X 2X  0 X+2 3X+2  0 2X 3X  X 2X 3X+2 2X 3X+2  2 3X 2X+2 3X  2 3X+2  2 X+2 3X+2 2X+2 X+2 2X+2  2  2 X+2  X  2  0 3X+2  X 2X  2  X 3X 2X 2X 3X+2 X+2 X+2  2 2X  X 3X+2 2X 3X+2  0  2  X 2X+2 2X+2  X 3X 2X+2  2 X+2 2X 2X+2 3X 2X 3X 2X 3X 2X  X 2X  X 2X+2 2X  0 2X X+2  0  X  2  X 3X  2 X+2 2X 2X  X 3X  X  X  X  2  2 2X+2 3X 2X
 0  0  X  X  0 3X+2 X+2 2X  2 3X+2 3X+2  2 3X  2 2X+2  X  2 X+2 3X 2X+2 X+2 X+2  2  0  0 2X X+2  X 3X+2  2 3X+2  0 2X  X 2X+2 3X  X  2 3X+2 2X 3X+2 2X+2 3X 2X+2 3X 2X X+2  2 3X 2X  2 2X  X  X 2X 3X+2  2 3X+2  X  X 2X 2X+2 3X+2  X 3X  0 3X+2 2X  2 2X+2  X 2X 3X X+2  2 3X  2  X  2 3X+2  0  0 X+2  2  X 2X 3X+2 X+2 3X  X X+2  X  X 3X 3X+2  2
 0  0  0  2  2 2X+2  0 2X+2  2 2X 2X+2  0  2 2X+2  0 2X  0 2X 2X+2  2  0  2  2  0  2 2X 2X+2  0 2X+2 2X+2 2X 2X 2X+2 2X+2  0  0 2X 2X  2  2  2 2X  0  2  2  2  0 2X 2X+2 2X 2X 2X+2  0 2X  0  2 2X+2  0 2X  2 2X 2X+2 2X 2X+2  2 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X  0 2X+2 2X  2  2  2 2X+2 2X 2X+2  0 2X 2X+2 2X+2  0 2X+2 2X  0  0 2X  0 2X 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+72x^90+256x^91+279x^92+408x^93+405x^94+472x^95+487x^96+506x^97+358x^98+288x^99+195x^100+124x^101+73x^102+84x^103+35x^104+14x^105+4x^106+20x^107+1x^108+4x^109+8x^110+1x^112+1x^156

The gray image is a code over GF(2) with n=768, k=12 and d=360.
This code was found by Heurico 1.16 in 1.5 seconds.