The generator matrix

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

generates a code of length 23 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+47x^16+56x^18+208x^20+184x^22+262x^24+136x^26+100x^28+8x^30+18x^32+4x^36

The gray image is a code over GF(2) with n=46, k=10 and d=16.
This code was found by Heurico 1.16 in 0.0326 seconds.