The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+47x^34+300x^35+1082x^36+2812x^37+4865x^38+7564x^39+10316x^40+11216x^41+10599x^42+8178x^43+4814x^44+2266x^45+885x^46+368x^47+125x^48+52x^49+18x^50+6x^51+12x^52+6x^53+2x^54+2x^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 21.9 seconds.