The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+63x^4+67x^6+506x^8+501x^10+2048x^11+910x^12+24576x^13+910x^14+2048x^15+501x^16+506x^18+67x^20+63x^22+1x^26

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 0.355 seconds.