The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+16x^22+58x^23+72x^24+74x^25+58x^26+28x^27+34x^28+38x^29+36x^30+36x^31+19x^32+14x^33+18x^34+4x^35+2x^36+2x^37+2x^39

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 0.0133 seconds.