The generator matrix

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

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+12x^21+26x^22+174x^24+16x^25+16x^26+4x^29+6x^30+1x^32

The gray image is a code over GF(2) with n=192, k=8 and d=84.
This code was found by Heurico 1.16 in 0.062 seconds.