The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+51x^18+148x^19+293x^20+504x^21+734x^22+1050x^23+1420x^24+1982x^25+2413x^26+2800x^27+3247x^28+3244x^29+3255x^30+3032x^31+2555x^32+2024x^33+1377x^34+1016x^35+715x^36+412x^37+224x^38+142x^39+88x^40+26x^41+7x^42+4x^43+1x^44+3x^46

The gray image is a code over GF(2) with n=58, k=15 and d=18.
This code was found by Heurico 1.10 in 14.4 seconds.