The generator matrix

 1  0  0  0  0  0  1  1  1  1  0  1  1  2  0  2  2  1  0  1  1  1  1  1
 0  1  0  0  0  0  2  1  3  1  1  0  2  1  1  2  0  0  2  2  1  2  0  0
 0  0  1  0  0  0  0  0  0  0  2  1  1  3  1  2  1  2  2  2  1  0  1  0
 0  0  0  1  0  0  1  3  2  2  3  1  0  3  0  1  2  3  2  1  1  3  1  0
 0  0  0  0  1  0  1  2  3  0  1  2  2  3  2  1  1  3  1  2  3  3  3  0
 0  0  0  0  0  1  1  0  0  3  3  2  3  3  1  3  3  2  0  1  3  2  3  0

generates a code of length 24 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+50x^16+60x^17+186x^18+194x^19+252x^20+324x^21+302x^22+458x^23+408x^24+412x^25+387x^26+374x^27+268x^28+156x^29+138x^30+62x^31+45x^32+8x^33+10x^34+1x^42

The gray image is a code over GF(2) with n=48, k=12 and d=16.
This code was found by Heurico 1.16 in 0.478 seconds.