The generator matrix

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

generates a code of length 28 over Z4 who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+40x^19+108x^20+180x^21+299x^22+414x^23+513x^24+536x^25+716x^26+816x^27+797x^28+898x^29+781x^30+688x^31+514x^32+326x^33+231x^34+144x^35+107x^36+42x^37+20x^38+10x^39+8x^40+2x^41+1x^42

The gray image is a code over GF(2) with n=56, k=13 and d=19.
This code was found by Heurico 1.16 in 2.5 seconds.