The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+101x^20+64x^21+704x^22+576x^23+1212x^24+576x^25+704x^26+64x^27+82x^28+11x^32+1x^36

The gray image is a code over GF(2) with n=192, k=12 and d=80.
This code was found by Heurico 1.16 in 0.078 seconds.