The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+169x^16+354x^18+694x^20+770x^22+928x^24+694x^26+342x^28+102x^30+38x^32+4x^36

The gray image is a code over GF(2) with n=46, k=12 and d=16.
This code was found by Heurico 1.16 in 0.417 seconds.