The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+206x^16+128x^18+560x^20+256x^22+576x^24+128x^26+176x^28+17x^32

The gray image is a code over GF(2) with n=44, k=11 and d=16.
This code was found by Heurico 1.16 in 0.132 seconds.