The generator matrix

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

generates a code of length 27 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+47x^20+76x^21+117x^22+162x^23+166x^24+164x^25+169x^26+222x^27+204x^28+180x^29+188x^30+142x^31+75x^32+60x^33+34x^34+18x^35+17x^36+3x^38+2x^40+1x^42

The gray image is a code over GF(2) with n=54, k=11 and d=20.
This code was found by Heurico 1.16 in 0.153 seconds.