The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+328x^16+968x^18+1931x^20+2928x^22+3837x^24+3320x^26+1930x^28+800x^30+281x^32+48x^34+11x^36+1x^40

The gray image is a code over GF(2) with n=48, k=14 and d=16.
This code was found by Heurico 1.16 in 74.4 seconds.