The generator matrix

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

generates a code of length 17 over Z16 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+100x^14+285x^16+256x^17+312x^18+32x^20+36x^22+2x^24

The gray image is a code over GF(2) with n=136, k=10 and d=56.
This code was found by Heurico 1.16 in 3.25 seconds.