The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  0  1  1  2  X  1  1  X  X
 0  X  2 3X+2  0 3X+2  2 3X  2 3X+2  0 2X 3X 3X+2 3X  X  0  0  X 3X 3X+2  2 3X+2 3X+2
 0  0 2X  0  0  0 2X  0  0  0 2X 2X 2X  0 2X 2X  0 2X  0  0 2X 2X  0  0
 0  0  0 2X  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X  0  0  0 2X  0 2X 2X 2X 2X
 0  0  0  0 2X  0 2X 2X 2X 2X  0 2X  0  0 2X  0  0 2X  0 2X 2X 2X 2X  0
 0  0  0  0  0 2X 2X  0 2X 2X  0  0 2X  0 2X 2X 2X  0  0  0 2X  0  0 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+88x^20+32x^21+272x^22+480x^23+309x^24+480x^25+272x^26+32x^27+73x^28+6x^32+3x^36

The gray image is a code over GF(2) with n=192, k=11 and d=80.
This code was found by Heurico 1.16 in 0.031 seconds.