The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  X  1  X  1 2X+2  1  X  1  1
 0  2  0  0  0 2X+2  2 2X+2  0 2X  2  2  0  2  2 2X+2  2 2X  0 2X 2X 2X+2  0  2
 0  0  2  0 2X+2 2X+2 2X+2 2X  0 2X 2X+2  2 2X+2 2X 2X+2 2X+2 2X  0 2X+2  2  2  0  2 2X+2
 0  0  0  2 2X+2 2X  2  2  0  2 2X  2  2  2 2X+2  0 2X+2 2X+2  0 2X+2 2X  2 2X  2
 0  0  0  0 2X 2X 2X 2X 2X 2X  0  0 2X  0  0 2X 2X 2X  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+141x^20+24x^21+154x^22+360x^23+732x^24+360x^25+126x^26+24x^27+74x^28+38x^30+11x^32+2x^34+1x^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 0.047 seconds.