The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  0  2  2 12  1  1  2  4  1  2  1  1  1  1  1  1  4  1  8  8  1  1
 0  2  0  6  0 14 10  8  6  8  2  8  0  8  6  2  6  2  2  6  2  2  4 14  2  2 12  6  2 12  2  4 12 14  2  0  2  2  0  0
 0  0 12  0  0  0  0  4  4  8  4  4  8 12  4  4  0  8  8  4 12  4  4  4  8 12  0  4  8 12  0  4  0 12  4  4  4  0  4  0
 0  0  0 12  0  8 12  0 12  4 12 12  4 12  0  8  0  0  4 12  8  8  0  8 12 12 12  8  0  4  0 12  8  4  0  0  8  8  4 12
 0  0  0  0 12 12  4 12  8  0 12  4 12  8 12  0  8 12 12  0  0 12  0  8  0  4 12 12  4  8  4  4  8  8  8  8  0 12  8  0

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

Homogenous weight enumerator: w(x)=1x^0+130x^34+76x^35+474x^36+476x^37+1052x^38+1240x^39+1396x^40+1240x^41+982x^42+476x^43+412x^44+76x^45+90x^46+41x^48+16x^50+10x^52+2x^54+2x^56

The gray image is a code over GF(2) with n=320, k=13 and d=136.
This code was found by Heurico 1.16 in 0.854 seconds.