The generator matrix

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

generates a code of length 22 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+124x^16+340x^18+335x^20+406x^22+465x^24+232x^26+121x^28+14x^30+10x^32

The gray image is a code over GF(2) with n=44, k=11 and d=16.
This code was found by Heurico 1.10 in 0.047 seconds.