The generator matrix

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

generates a code of length 29 over Z4 who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+111x^18+220x^19+532x^20+792x^21+1368x^22+1950x^23+2882x^24+3868x^25+4965x^26+5962x^27+6456x^28+7088x^29+6482x^30+6156x^31+5079x^32+3864x^33+3001x^34+1872x^35+1332x^36+728x^37+436x^38+214x^39+102x^40+44x^41+19x^42+10x^43+2x^46

The gray image is a code over GF(2) with n=58, k=16 and d=18.
This code was found by Heurico 1.10 in 55.8 seconds.