The generator matrix

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

generates a code of length 27 over Z4 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+70x^22+103x^24+91x^26+98x^28+78x^30+47x^32+12x^34+6x^36+4x^38+1x^40+1x^42

The gray image is a code over GF(2) with n=54, k=9 and d=22.
This code was found by Heurico 1.16 in 2.41 seconds.