The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+349x^34+1016x^35+2751x^36+4496x^37+7983x^38+10400x^39+11689x^40+10296x^41+8097x^42+4584x^43+2393x^44+880x^45+461x^46+64x^47+58x^48+8x^49+6x^50+4x^52

The gray image is a code over GF(2) with n=320, k=16 and d=136.
This code was found by Heurico 1.16 in 21.7 seconds.