The generator matrix

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

generates a code of length 40 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+151x^34+160x^35+601x^36+1140x^37+2092x^38+2556x^39+3139x^40+2504x^41+1980x^42+1176x^43+545x^44+132x^45+120x^46+12x^47+52x^48+9x^50+14x^52

The gray image is a code over GF(2) with n=320, k=14 and d=136.
This code was found by Heurico 1.16 in 2.09 seconds.