The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+81x^20+90x^21+171x^22+222x^23+271x^24+290x^25+317x^26+390x^27+358x^28+446x^29+355x^30+346x^31+253x^32+182x^33+154x^34+66x^35+57x^36+16x^37+25x^38+3x^40+1x^42+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 0.624 seconds.