The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+24x^20+110x^21+177x^22+222x^23+281x^24+296x^25+346x^26+374x^27+394x^28+400x^29+373x^30+350x^31+267x^32+208x^33+118x^34+74x^35+54x^36+10x^37+9x^38+4x^39+3x^40+1x^46

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 0.651 seconds.