The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+68x^8+166x^9+354x^10+686x^11+1063x^12+1800x^13+2632x^14+3432x^15+4153x^16+4228x^17+3964x^18+3380x^19+2574x^20+1864x^21+1192x^22+680x^23+322x^24+134x^25+50x^26+14x^27+11x^28

The gray image is a code over GF(2) with n=34, k=15 and d=8.
This code was found by Heurico 1.16 in 7.19 seconds.