The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+222x^20+96x^21+552x^22+672x^23+1062x^24+672x^25+500x^26+96x^27+178x^28+32x^30+9x^32+4x^34

The gray image is a code over GF(2) with n=192, k=12 and d=80.
This code was found by Heurico 1.16 in 2.7 seconds.