The generator matrix

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

generates a code of length 16 over Z4 who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+58x^7+209x^8+456x^9+966x^10+1912x^11+3373x^12+5276x^13+7172x^14+8696x^15+9347x^16+8668x^17+7104x^18+5252x^19+3434x^20+1940x^21+988x^22+462x^23+147x^24+44x^25+26x^26+4x^27+1x^28

The gray image is a code over GF(2) with n=32, k=16 and d=7.
This code was found by Heurico 1.10 in 4.29 seconds.