The generator matrix

1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 2 1 1 1 1 0 1 2 0 0 0 1 1
0 1 0 0 0 0 0 0 0 0 0 0 1 3 2 1 3 1 2 1 1 2 1 0 2 1 1 0
0 0 1 0 0 0 0 0 1 1 2 3 0 1 3 1 1 0 2 2 2 1 0 0 2 2 0 0
0 0 0 1 0 0 0 0 1 2 1 0 2 3 3 1 0 2 1 0 2 1 3 1 1 0 3 0
0 0 0 0 1 0 0 0 1 3 3 2 1 2 2 3 0 0 0 1 1 0 0 3 1 2 1 0
0 0 0 0 0 1 0 1 0 1 3 3 2 1 2 1 2 1 0 1 3 0 1 1 0 2 1 0
0 0 0 0 0 0 1 1 3 1 2 0 0 1 1 0 3 2 0 3 1 0 0 1 2 1 0 0
0 0 0 0 0 0 0 2 2 0 2 2 2 2 0 2 2 0 2 0 2 0 2 2 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+44x^17+131x^18+282x^19+462x^20+698x^21+1009x^22+1464x^23+1953x^24+2342x^25+2959x^26+3354x^27+3340x^28+3216x^29+2954x^30+2620x^31+2013x^32+1396x^33+1009x^34+666x^35+398x^36+230x^37+125x^38+60x^39+25x^40+10x^41+5x^42+2x^43

The gray image is a code over GF(2) with n=56, k=15 and d=17.
This code was found by Heurico 1.10 in 13 seconds.