The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+38x^22+50x^23+82x^24+44x^25+32x^26+2x^27+5x^28+1x^30+1x^34

The gray image is a code over GF(2) with n=192, k=8 and d=88.
This code was found by Heurico 1.16 in -1.01e-007 seconds.