The generator matrix

 1  1  1  1  1  1  1  1  2  8  1  1  8  1  0  1  2
 0  2  0  6  8  6  0  2  6  2 10  2  2  4  2  2 10
 0  0 12  0  8  4  4 12  0  0 12  8 12  0  4  8 12
 0  0  0 12 12  4 12  0  8 12  4  4  8  4 12  0  4

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

Homogenous weight enumerator: w(x)=1x^0+132x^14+192x^15+457x^16+512x^17+442x^18+192x^19+96x^20+16x^22+6x^24+2x^26

The gray image is a code over GF(2) with n=136, k=11 and d=56.
This code was found by Heurico 1.16 in 11.2 seconds.