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

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

Homogenous weight enumerator: w(x)=1x^0+79x^90+278x^91+247x^92+306x^93+453x^94+434x^95+690x^96+372x^97+400x^98+290x^99+181x^100+122x^101+77x^102+86x^103+31x^104+32x^105+15x^106+1x^108+1x^164

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 1.52 seconds.