The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  1  2  1  1  1  2  1  1
 0  2  0  0  0  0  0  0  0  0  2  2  0  0  2  0  0  2  2  2  0  2  2  2  0  0  0  2
 0  0  2  0  0  0  0  0  0  2  2  2  0  2  2  2  2  2  2  0  2  0  2  0  0  2  2  2
 0  0  0  2  0  0  0  0  0  2  0  2  2  2  0  2  0  0  0  0  2  2  2  0  2  2  0  2
 0  0  0  0  2  0  0  0  2  0  0  2  2  0  0  0  2  2  0  2  0  2  0  2  0  2  2  0
 0  0  0  0  0  2  0  0  2  0  2  0  0  2  0  2  2  0  2  0  2  0  0  2  2  2  0  2
 0  0  0  0  0  0  2  0  2  2  2  0  0  0  2  0  2  2  0  0  2  2  2  0  2  0  0  2
 0  0  0  0  0  0  0  2  2  2  0  0  2  2  0  0  2  2  2  0  0  0  2  0  2  2  0  0

generates a code of length 28 over Z4 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+46x^22+83x^24+64x^26+96x^28+132x^30+70x^32+14x^38+5x^40+1x^48

The gray image is a code over GF(2) with n=56, k=9 and d=22.
This code was found by Heurico 1.16 in 26.1 seconds.