The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+337x^20+280x^21+812x^22+200x^23+829x^24+344x^25+744x^26+152x^27+299x^28+48x^29+44x^30+6x^32

The gray image is a code over GF(2) with n=96, k=12 and d=40.
This code was found by Heurico 1.16 in 35.9 seconds.