The generator matrix

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

generates a code of length 13 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+93x^4+288x^6+1196x^8+2416x^10+4282x^12+3952x^14+2713x^16+976x^18+409x^20+48x^22+10x^24

The gray image is a code over GF(2) with n=26, k=14 and d=4.
This code was found by Heurico 1.16 in 0.829 seconds.