The generator matrix

 1  0  1  1  1  6  1  1  8  1 14  1 12  1  1  1 10  1  1  4  1  1  2  0  1  1  4  6  8  1 14  1  1 10  1  1  2  1  2  1  1
 0  1 11  6 13  1 12  7  1 10  1  1  1  3  8  5  1 14 15  1  4  2  1  1  3  9  1  1  1  5  1  8 14  1  9  2  8 13  2  1  0
 0  0 12  0  4  0  0  4  4  8 12  4  8  0 12  0  8  4  0  4 12 12 12  8  0  8 12  8 12  8 12 12 12  8  8 12  4  4  4 12  0
 0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  0  0  8  8  0  0  0  8  0  8  8  8  0  8  8  0  8  0  0  8  0  0  8  8  0
 0  0  0  0  8  0  0  8  8  0  0  0  0  0  0  8  8  8  8  8  0  8  0  8  8  8  0  0  8  0  0  0  8  8  0  0  8  0  8  0  8
 0  0  0  0  0  8  0  8  8  8  8  0  8  8  0  0  8  8  8  0  0  0  0  0  8  8  8  8  0  0  0  8  0  8  0  0  8  8  8  8  8
 0  0  0  0  0  0  8  0  0  8  0  0  0  8  8  8  0  8  0  8  8  8  8  0  0  8  8  8  0  8  8  8  0  8  0  0  8  8  8  8  0

generates a code of length 41 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+32x^34+108x^35+230x^36+552x^37+1300x^38+1696x^39+3078x^40+2488x^41+3050x^42+1680x^43+1249x^44+520x^45+210x^46+96x^47+41x^48+24x^49+14x^50+4x^51+8x^52+2x^54+1x^60

The gray image is a code over GF(2) with n=328, k=14 and d=136.
This code was found by Heurico 1.16 in 1.99 seconds.