The generator matrix

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

generates a code of length 17 over Z4 who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+54x^7+169x^8+382x^9+712x^10+1254x^11+2315x^12+3660x^13+5049x^14+6600x^15+7895x^16+8472x^17+8132x^18+6968x^19+5450x^20+3892x^21+2414x^22+1234x^23+551x^24+234x^25+76x^26+18x^27+3x^28+1x^30

The gray image is a code over GF(2) with n=34, k=16 and d=7.
This code was found by Heurico 1.10 in 4.46 seconds.