The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+50x^20+80x^21+172x^22+238x^23+256x^24+306x^25+335x^26+400x^27+398x^28+414x^29+367x^30+312x^31+259x^32+206x^33+167x^34+72x^35+28x^36+18x^37+13x^38+2x^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 1.16 in 0.649 seconds.