The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  1  1  X  1  1  1  1 2X+2  1  1  X  X  1
 0  2  0  2  0  2  0 2X+2 2X  2  0  0  2  2  2 2X+2  2  2  2 2X  0  2  2  0
 0  0 2X  0  0  0  0  0 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0
 0  0  0 2X  0  0  0 2X  0  0 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0
 0  0  0  0 2X  0  0  0  0 2X 2X 2X  0 2X  0  0 2X 2X  0  0 2X  0 2X  0
 0  0  0  0  0 2X  0 2X  0 2X 2X  0 2X  0 2X  0  0 2X  0 2X 2X  0 2X 2X
 0  0  0  0  0  0 2X  0 2X 2X  0 2X 2X 2X 2X  0  0  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 18.

Homogenous weight enumerator: w(x)=1x^0+19x^18+16x^19+57x^20+48x^21+115x^22+448x^23+656x^24+448x^25+100x^26+48x^27+46x^28+16x^29+20x^30+7x^32+1x^34+1x^36+1x^38

The gray image is a code over GF(2) with n=192, k=11 and d=72.
This code was found by Heurico 1.16 in 0.032 seconds.