The generator matrix

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

generates a code of length 22 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+71x^20+46x^24+8x^28+1x^32+1x^36

The gray image is a code over GF(2) with n=44, k=7 and d=20.
This code was found by Heurico 1.16 in 0.0504 seconds.