The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+171x^16+474x^18+953x^20+1472x^22+1996x^24+1476x^26+1106x^28+400x^30+118x^32+18x^34+5x^36+2x^40

The gray image is a code over GF(2) with n=48, k=13 and d=16.
This code was found by Heurico 1.16 in 1.81 seconds.