The generator matrix

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

generates a code of length 21 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+111x^16+202x^18+210x^20+196x^22+194x^24+82x^26+26x^28+2x^32

The gray image is a code over GF(2) with n=42, k=10 and d=16.
This code was found by Heurico 1.10 in 0.016 seconds.