The generator matrix

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

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+65x^90+182x^91+252x^92+172x^93+268x^94+146x^95+199x^96+148x^97+120x^98+106x^99+74x^100+60x^101+76x^102+30x^103+31x^104+22x^105+35x^106+12x^107+14x^108+12x^109+10x^110+4x^112+2x^113+4x^115+2x^118+1x^120

The gray image is a code over GF(2) with n=384, k=11 and d=180.
This code was found by Heurico 1.16 in 0.773 seconds.