The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+436x^90+793x^92+792x^94+663x^96+482x^98+367x^100+176x^102+151x^104+110x^106+64x^108+44x^110+9x^112+8x^114

The gray image is a code over GF(2) with n=384, k=12 and d=180.
This code was found by Heurico 1.16 in 3.09 seconds.