The generator matrix

 1  1  1  1  1  1  1  1  2  0  1  1  2  4  1  2  1
 0  2  0  6  4  6 12  2  6  2  8  6 12 12  6  4  8
 0  0 12  0  4  0  0  8  8  4  0  4 12 12  4  8  0
 0  0  0 12  0  0  8  4  8  4 12 12  0  4  4 12 12
 0  0  0  0  8  8  8  8  0  0  8  0  0  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+138x^13+100x^14+484x^15+669x^16+1326x^17+696x^18+472x^19+32x^20+134x^21+36x^22+4x^23+2x^24+2x^25

The gray image is a code over GF(2) with n=136, k=12 and d=52.
This code was found by Heurico 1.16 in 13.2 seconds.