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 0
0 0 1 0 1 0 2 3 1 1 0 1 2 2 3 3 0 1 2 2 1 1 0 1 0 1 2
0 0 0 1 1 3 3 2 0 1 2 3 1 3 0 0 3 2 1 2 2 3 1 1 0 0 1
0 0 0 0 2 2 2 0 0 0 2 2 0 0 2 2 2 2 2 2 2 0 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+24x^22+52x^23+66x^24+72x^25+56x^26+44x^27+30x^28+36x^29+32x^30+28x^31+29x^32+16x^33+16x^34+4x^35+2x^36+4x^37

The gray image is a code over GF(2) with n=54, k=9 and d=22.
This code was found by Heurico 1.10 in 0 seconds.