The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+60x^20+72x^21+126x^22+168x^23+162x^24+188x^25+163x^26+188x^27+176x^28+192x^29+149x^30+128x^31+129x^32+60x^33+37x^34+28x^35+16x^36+5x^38

The gray image is a code over GF(2) with n=54, k=11 and d=20.
This code was found by Heurico 1.10 in 0.047 seconds.