The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+39x^16+54x^17+141x^18+146x^19+159x^20+210x^21+156x^22+222x^23+190x^24+202x^25+178x^26+126x^27+118x^28+46x^29+36x^30+18x^31+2x^32+1x^34+3x^36

The gray image is a code over GF(2) with n=46, k=11 and d=16.
This code was found by Heurico 1.10 in 0.047 seconds.