The generator matrix

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

generates a code of length 29 over Z4 who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+50x^17+141x^18+340x^19+519x^20+872x^21+1396x^22+1970x^23+3023x^24+3932x^25+4863x^26+5846x^27+6402x^28+6712x^29+6487x^30+5900x^31+4845x^32+3874x^33+3107x^34+2056x^35+1335x^36+880x^37+490x^38+258x^39+131x^40+64x^41+25x^42+14x^43+3x^46

The gray image is a code over GF(2) with n=58, k=16 and d=17.
This code was found by Heurico 1.10 in 52 seconds.