The generator matrix

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

generates a code of length 17 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+78x^8+178x^9+331x^10+632x^11+1094x^12+1848x^13+2616x^14+3512x^15+4069x^16+4092x^17+4086x^18+3384x^19+2604x^20+1944x^21+1088x^22+648x^23+340x^24+130x^25+71x^26+16x^27+6x^28

The gray image is a code over GF(2) with n=34, k=15 and d=8.
This code was found by Heurico 1.10 in 1.73 seconds.