The generator matrix

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

generates a code of length 16 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+168x^6+38x^7+678x^8+466x^9+2228x^10+1948x^11+4053x^12+5316x^13+5945x^14+8632x^15+6661x^16+8568x^17+5852x^18+5348x^19+4130x^20+1980x^21+2182x^22+418x^23+724x^24+54x^25+136x^26+9x^28+1x^30

The gray image is a code over GF(2) with n=32, k=16 and d=6.
This code was found by Heurico 1.10 in 1.99 seconds.