The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  2  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  0
 0  0  0  0  0  0  0  0  2  0  0  0  0  2  0  0  0
 0  0  0  0  0  0  0  0  0  2  0  0  0  2  0  0  0
 0  0  0  0  0  0  0  0  0  0  2  0  0  2  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  2  0  2  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  0  2  2  0  0  0

generates a code of length 17 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+78x^4+715x^8+13x^10+1716x^12+286x^14+1287x^16+8192x^17+1287x^18+286x^20+1716x^22+13x^24+715x^26+78x^30+1x^34

The gray image is a code over GF(2) with n=34, k=14 and d=4.
This code was found by Heurico 1.16 in 0.739 seconds.