The generator matrix

 1  1  1  1  2  2  2  1  1  1  1  1  1
 0 12  0  4  0  4 12  0  0  0  0  0  0
 0  0 12  4 12  4  0  0  0  0  0  0  0
 0  0  0  8  0  0  0  0  0  0  8  0  0
 0  0  0  0  8  0  0  0  0  0  8  0  0
 0  0  0  0  0  8  0  0  0  0  8  0  0
 0  0  0  0  0  0  8  0  0  0  8  0  0
 0  0  0  0  0  0  0  8  0  0  8  0  0
 0  0  0  0  0  0  0  0  8  0  8  0  0
 0  0  0  0  0  0  0  0  0  8  8  0  0

generates a code of length 13 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+69x^4+144x^6+580x^8+1016x^10+1536x^11+2370x^12+21504x^13+2040x^14+1536x^15+1313x^16+360x^18+265x^20+24x^22+10x^24

The gray image is a code over GF(2) with n=104, k=15 and d=16.
This code was found by Heurico 1.16 in 0.327 seconds.