The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  1  1
 0  1  0  1  0  1  1  0  0  0  0  0  0
 0  0  1  1  1  0  1  0  0  0  0  0  0
 0  0  0  2  0  0  0  0  0  0  2  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+69x^4+144x^6+580x^8+1016x^10+2370x^12+2040x^14+1313x^16+360x^18+265x^20+24x^22+10x^24

The gray image is a code over GF(2) with n=26, k=13 and d=4.
This code was found by Heurico 1.16 in 0.126 seconds.