The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  4  2  2  1  2  0  8  2  1  2 12  2  2  4  1  1  1  1
 0  2  0  0  0  2  6 14  0  8  0  0  6 10 12  6 14  8  2  4 10 10 10  2 10  4  6 10  2  4 14  2  6  2  6  8  2 12  6  4  8
 0  0  2  0  2  2  2  0  4 14  8 14 10  8  2 14 12 12 10  6  8  2  8  4  6  6  8  8  4  2 14 12  4 10 12  0 10  8  6  6  8
 0  0  0  2  2  0  2 10  8  2 14  4  4  2  6 14  0 10  2  8  6  4  0  0  8  4 14  6 10  6 10 12 12  0 12  6 12  4  4 12 14
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  0  8  8  0  8  0  8  0  0  8  8  0  8  8  0  8
 0  0  0  0  0  8  0  8  8  8  8  8  0  0  0  8  0  0  8  8  0  0  8  0  0  0  8  8  0  8  8  0  8  0  8  0  0  0  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+152x^34+418x^35+906x^36+1244x^37+2415x^38+3368x^39+5029x^40+5774x^41+5006x^42+3516x^43+2351x^44+1128x^45+763x^46+370x^47+222x^48+46x^49+45x^50+6x^51+3x^52+2x^54+2x^55+1x^58

The gray image is a code over GF(2) with n=328, k=15 and d=136.
This code was found by Heurico 1.16 in 9.94 seconds.