The generator matrix

 1  1  1  1  1  1  1  1  2  0  1  1  1  1  2  1  1
 0  2  6  6  0 12  2  8 14  2  6 14  2  2 12  8  0
 0  0 12  0  0  0  4  4  4  8  8  4  8  0 12  4  4
 0  0  0  8  0  8  8  8  8  8  0  0  0  8  0  0  0
 0  0  0  0  8  8  0  0  0  8  8  8  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+178x^14+582x^16+512x^17+644x^18+87x^20+42x^22+1x^24+1x^28

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 16.6 seconds.