The generator matrix

 1  0  1  1  1  6  1  1  8  1  1  0  1  1  1  4  1
 0  1 11  6 13  1  8  3  1 14  3  1  6 13 10  1  3
 0  0 12  0  4  8  8 12  0  4  0  4 12  8  0  0  4
 0  0  0 12  0  8  4 12  4  0  8  4  4 12  0  4 12
 0  0  0  0  8  8  8  0  8  0  0  8  0  0  8  0  8

generates a code of length 17 over Z16 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+72x^13+292x^14+616x^15+2013x^16+2224x^17+2040x^18+592x^19+224x^20+72x^21+36x^22+8x^23+2x^24

The gray image is a code over GF(2) with n=136, k=13 and d=52.
This code was found by Heurico 1.16 in 17 seconds.