The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+48x^16+44x^17+115x^18+184x^19+173x^20+176x^21+169x^22+228x^23+185x^24+172x^25+183x^26+160x^27+95x^28+56x^29+43x^30+4x^31+10x^32+2x^34

The gray image is a code over GF(2) with n=46, k=11 and d=16.
This code was found by Heurico 1.16 in 0.11 seconds.