The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+54x^16+64x^17+153x^18+196x^19+289x^20+318x^21+335x^22+408x^23+347x^24+498x^25+392x^26+356x^27+297x^28+130x^29+131x^30+64x^31+34x^32+14x^33+10x^34+2x^36+2x^38+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 0.451 seconds.