The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X+2 3X  0  2 3X  1  1  1  2 2X+2  1  1  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  1  1  1  1  0 3X 3X+2  X  X  2  0 2X
 0  0 2X  0 2X  0  0 2X  0  0 2X  0 2X  0  0 2X 2X  0 2X 2X 2X  0  0 2X
 0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X  0  0 2X 2X  0 2X  0  0 2X  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+249x^22+128x^23+283x^24+128x^25+224x^26+3x^28+6x^30+1x^36+1x^38

The gray image is a code over GF(2) with n=192, k=10 and d=88.
This code was found by Heurico 1.16 in 2.02 seconds.