The generator matrix

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

generates a code of length 28 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+56x^20+92x^21+150x^22+218x^23+270x^24+316x^25+343x^26+386x^27+404x^28+416x^29+351x^30+338x^31+277x^32+188x^33+135x^34+78x^35+48x^36+12x^37+11x^38+4x^39+2x^42

The gray image is a code over GF(2) with n=56, k=12 and d=20.
This code was found by Heurico 1.10 in 0.25 seconds.