The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+218x^34+512x^35+1417x^36+2508x^37+4461x^38+7760x^39+9615x^40+12680x^41+9397x^42+7940x^43+4572x^44+2412x^45+1241x^46+424x^47+251x^48+64x^49+41x^50+4x^51+15x^52+2x^54+1x^56

The gray image is a code over GF(2) with n=328, k=16 and d=136.
This code was found by Heurico 1.16 in 26.7 seconds.