The generator matrix

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

generates a code of length 30 over Z4 who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+46x^18+168x^19+351x^20+560x^21+920x^22+1460x^23+2112x^24+3074x^25+3886x^26+4704x^27+5721x^28+6342x^29+6563x^30+6464x^31+5907x^32+4796x^33+3902x^34+3040x^35+2105x^36+1476x^37+858x^38+524x^39+300x^40+130x^41+78x^42+24x^43+15x^44+6x^45+3x^46

The gray image is a code over GF(2) with n=60, k=16 and d=18.
This code was found by Heurico 1.10 in 52 seconds.