The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+173x^34+116x^35+652x^36+832x^37+2383x^38+3808x^39+5640x^40+5876x^41+5356x^42+3732x^43+2393x^44+904x^45+570x^46+88x^47+156x^48+4x^49+59x^50+19x^52+3x^54+3x^56

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 9.57 seconds.