The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  2  0  0  0  2  0  0  2  1  1  2  0  2  2  0  1
 0  1  0  1  0  1  1  0  2  1  3  1  1  0  1  1  1  1  0  2  0  0  0  2  2  0  0  0
 0  0  1  1  1  0  1  0  1  3  2  0  1  1  0  2  1  3  1  1  0  3  1  1  1  1  1  0
 0  0  0  2  0  0  0  0  0  2  0  2  2  2  0  2  0  2  0  0  2  2  2  2  2  2  2  0
 0  0  0  0  2  0  0  0  2  0  0  2  2  2  0  2  2  0  0  0  0  2  0  0  0  2  2  0
 0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  0  0  2  0  2  2  0  0  0  2  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  2  0  2  0  2  0  2  0  2  0
 0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  2  0  2  2  2  0  0  0  0  0  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+29x^20+24x^21+119x^22+120x^23+128x^24+136x^25+139x^26+232x^27+192x^28+232x^29+153x^30+136x^31+137x^32+120x^33+84x^34+24x^35+19x^36+15x^38+6x^40+1x^42+1x^46

The gray image is a code over GF(2) with n=56, k=11 and d=20.
This code was found by Heurico 1.16 in 0.158 seconds.