The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2 12  2  2  0  1  8  1  1  1  1  4  1  1  2 12  0  1  2  2  2  4  1  1
 0  2  0  2  0  0  6  6  4  4 10  6 12  4 14 14  4 10  2  6  4  2  2  2  2  6  0 12  4  2  0 12  8  2  6  2 14  4  2  4  4
 0  0  2  2 12  6  6  0 12  2 14 12  0  6  6  4 12  6  6  0  2  0  4  2 10 12  8  0  2  6  6 10  2  6 10  4  4 14  4 14  2
 0  0  0  8  0  0  0  0  8  0  0  8  8  0  8  8  8  0  8  8  0  0  0  8  0  8  8  8  0  8  0  0  0  8  0  8  0  8  8  0  8
 0  0  0  0  8  0  0  8  0  8  8  0  0  8  8  8  8  0  0  8  0  0  0  8  8  8  0  0  8  8  8  8  0  0  0  8  0  8  0  0  8
 0  0  0  0  0  8  0  0  0  8  8  8  8  0  8  8  0  0  0  0  8  0  8  8  0  8  0  8  0  8  8  8  0  0  8  0  8  8  8  0  0
 0  0  0  0  0  0  8  0  8  0  8  8  8  0  0  8  8  8  0  8  8  8  8  8  0  0  0  0  8  8  8  0  8  8  8  0  0  8  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+73x^34+148x^35+570x^36+524x^37+1520x^38+1396x^39+2924x^40+2042x^41+3067x^42+1386x^43+1496x^44+490x^45+444x^46+130x^47+121x^48+14x^49+11x^50+10x^51+6x^52+2x^53+4x^54+2x^55+2x^56+1x^58

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 2.79 seconds.