The generator matrix

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

generates a code of length 17 over Z4 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+70x^10+272x^12+648x^14+1057x^16+1057x^18+648x^20+272x^22+70x^24+1x^34

The gray image is a code over GF(2) with n=34, k=12 and d=10.
This code was found by Heurico 1.16 in 66.2 seconds.