The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+585x^34+2152x^35+5069x^36+9668x^37+15171x^38+21516x^39+22293x^40+22160x^41+15507x^42+9536x^43+4661x^44+1892x^45+623x^46+140x^47+70x^48+8x^49+16x^50+2x^52+2x^54

The gray image is a code over GF(2) with n=320, k=17 and d=136.
This code was found by Heurico 1.16 in 90 seconds.