The generator matrix

 1  0  1  1  1  4  1  1  6  1  1  2  8  1  1  1 10  1  1  1  0  1  1 14  1  1  1 12  2  8  1  4  1  1  2  1  4 10  1  1  1
 0  1  1  4  3  1  2  7  1  6  5  1  1  8  9  0  1 15  6  7  1 13 10  1  3 10  6  1  4  2  8  1  7  1  0 14  1  1  6  8  7
 0  0  2  2  0  2  2 10  0  0  8  2  4  4  0  6  6  6  6  4  6 10  8  4 14  6  8  0  2  2  2 12  4 12  6 10  2  8  6 10  2
 0  0  0  8  0  0  0  8  8  0  0  8  8  0  8  8  8  0  0  8  0  0  8  8  8  0  8  0  0  8  0  8  8  0  0  8  8  8  8  8  8
 0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  8  8  0  0  8  8  8  8  0  8  8  0  8  8  8  0  0  8  8  0  8  0  8  8
 0  0  0  0  0  8  0  0  0  8  8  0  8  8  8  8  0  0  8  0  8  8  0  0  0  8  8  0  0  0  0  0  8  0  8  8  8  8  0  8  8
 0  0  0  0  0  0  8  8  8  0  0  8  8  0  8  0  8  0  8  0  8  0  0  0  0  8  0  8  0  8  0  8  0  0  8  8  0  8  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+39x^34+288x^35+435x^36+1464x^37+1991x^38+4558x^39+4211x^40+6884x^41+4236x^42+4550x^43+1933x^44+1428x^45+363x^46+202x^47+70x^48+76x^49+24x^50+2x^51+4x^52+4x^53+2x^54+2x^56+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 7.09 seconds.