The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+43x^16+38x^17+91x^18+114x^19+84x^20+120x^21+75x^22+100x^23+96x^24+86x^25+75x^26+42x^27+32x^28+12x^29+13x^30+2x^34

The gray image is a code over GF(2) with n=44, k=10 and d=16.
This code was found by Heurico 1.10 in 0.016 seconds.