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  X  1  1  1  1  1 2X  1  1  1  1  2  1  1  X  1  1  1  1  2  1  X  1 2X  1  X 2X+2  X  1  1  1  X  X 2X+2  X
 0  X  0 3X+2  2 X+2 2X+2  X 2X X+2  0 X+2  2  X  2 3X 2X+2  X 2X+2 X+2  2 3X  0  X 2X 3X  0 3X+2  2 X+2  0  X 2X+2  X 3X  2  0  X  2  X 3X  0 X+2 2X 3X 2X+2  X 2X+2  2 3X+2 2X+2 X+2 2X+2 X+2 2X 2X 3X+2  0 X+2  2 X+2 3X+2  X 3X+2  2  X  X  X  X 2X 3X 2X  X 3X  2  0  2  0 2X X+2  2 X+2 3X  2  X 3X+2 3X+2  X 3X+2 2X  0  0 X+2 X+2  X X+2
 0  0 2X+2  0  2 2X 2X 2X  0  2  2  2  2 2X+2  0 2X+2  2  2  2  0  0  0  0  2 2X 2X  2 2X  0  2 2X+2 2X+2 2X+2  2 2X  2 2X  2  0 2X  0 2X 2X+2 2X+2  2 2X  0  0 2X+2  2  0 2X+2 2X+2  0  0 2X 2X 2X+2 2X  2  2  2 2X+2  0  2 2X+2  0 2X  0  2 2X  2  0 2X 2X+2  2 2X+2 2X  2 2X+2  2 2X  0  0 2X+2 2X  0 2X  0 2X+2  2  2 2X+2  2  0 2X
 0  0  0 2X+2  0  0  0 2X+2  2  2 2X+2  0 2X+2 2X  2 2X+2  2 2X 2X  0 2X+2 2X+2 2X 2X+2 2X+2  0  2  2  0 2X+2 2X  0  2  2  2 2X  2  0 2X  0 2X 2X 2X 2X+2  2  2  2 2X+2  0  0  0 2X 2X+2  2 2X 2X+2 2X+2  2  0  0 2X+2 2X  2 2X  2 2X+2  0  2  2  0  2 2X+2 2X+2 2X+2  0  2 2X  2  0  0 2X 2X  0  2 2X  2 2X+2 2X  2  2  0 2X  2  0  0 2X
 0  0  0  0 2X 2X 2X 2X  0 2X  0  0 2X 2X 2X  0 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X  0  0 2X  0 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0  0  0 2X 2X  0  0  0 2X 2X 2X  0  0  0  0  0  0 2X 2X  0 2X 2X 2X 2X 2X  0 2X  0  0  0 2X  0  0  0 2X 2X  0  0  0 2X 2X 2X 2X  0 2X 2X 2X  0  0  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+257x^90+32x^91+321x^92+144x^93+654x^94+320x^95+744x^96+352x^97+558x^98+160x^99+249x^100+16x^101+188x^102+54x^104+33x^106+5x^108+6x^110+1x^112+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 15.5 seconds.