The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+195x^34+1304x^35+2757x^36+5232x^37+7228x^38+10246x^39+11096x^40+10964x^41+7507x^42+5184x^43+2323x^44+960x^45+342x^46+142x^47+29x^48+12x^49+8x^50+4x^51+2x^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.