The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+59x^20+62x^21+96x^22+164x^23+179x^24+196x^25+206x^26+196x^27+144x^28+192x^29+166x^30+140x^31+115x^32+60x^33+42x^34+12x^35+13x^36+2x^37+2x^38+1x^40

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 0.154 seconds.