The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+180x^16+382x^18+668x^20+764x^22+909x^24+656x^26+380x^28+116x^30+37x^32+2x^34+1x^40

The gray image is a code over GF(2) with n=46, k=12 and d=16.
This code was found by Heurico 1.10 in 0.188 seconds.