The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+101x^8+176x^10+780x^12+1176x^14+1939x^16+1624x^18+1464x^20+584x^22+295x^24+24x^26+28x^28

The gray image is a code over GF(2) with n=34, k=13 and d=8.
This code was found by Heurico 1.16 in 0.354 seconds.