The generator matrix

 1  0  0  0  1  1  1  0  1  1  2  0  1  1  2  1  1  1  2  1  0  0
 0  1  0  0  0  1  1  1  3  1  1  1  0  1  2  3  0  0  1  1  1  1
 0  0  1  0  1  1  0  1  1  2  0  1  2  1  1  1  3  2  1  2  3  2
 0  0  0  1  1  0  1  1  1  0  1  2  3  0  3  3  0  2  1  0  1  3
 0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  0  0  2  2  0  2  2
 0  0  0  0  0  2  0  2  0  2  2  0  0  0  0  2  2  0  2  0  0  2
 0  0  0  0  0  0  2  2  0  2  0  2  0  2  2  2  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+122x^16+292x^18+398x^20+420x^22+436x^24+236x^26+128x^28+12x^30+1x^32+2x^36

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 0.131 seconds.