The generator matrix

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

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+456x^20+1012x^22+1228x^24+920x^26+440x^28+20x^30+19x^32

The gray image is a code over GF(2) with n=96, k=12 and d=40.
This code was found by Heurico 1.11 in 3.67 seconds.