The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+66x^21+111x^22+302x^23+117x^24+284x^25+73x^26+28x^27+10x^28+18x^29+7x^30+6x^31+1x^42

The gray image is a code over GF(2) with n=192, k=10 and d=84.
This code was found by Heurico 1.16 in 0.032 seconds.