The generator matrix

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

generates a code of length 28 over Z4 who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+38x^17+80x^18+164x^19+304x^20+428x^21+597x^22+766x^23+925x^24+1162x^25+1341x^26+1518x^27+1608x^28+1508x^29+1450x^30+1224x^31+997x^32+822x^33+538x^34+380x^35+240x^36+128x^37+81x^38+42x^39+21x^40+10x^41+9x^42+2x^43

The gray image is a code over GF(2) with n=56, k=14 and d=17.
This code was found by Heurico 1.10 in 3.38 seconds.