The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+21x^16+72x^18+106x^20+116x^22+108x^24+64x^26+14x^28+4x^30+6x^32

The gray image is a code over GF(2) with n=44, k=9 and d=16.
This code was found by Heurico 1.16 in 0.00988 seconds.