The generator matrix

 1  0  1  1  6  1  1  4  1  2  1  1  1  1  8  1  1  0  1 14  1 10  1  1  1  1  1 14  1  1  1  2  1  2  1  2 14  2  2  1
 0  1  1  6  1  3  5  1  4  1 15  4 10 15  1  8 13  1 11  1  2  1  7  2 13 11 14  1  0 10  8 10 11  1  8  0  1 12  8  0
 0  0  2  0  0  0  8  2  2  2  6 12  6  8 12  2 10 14  2  2 12  8 12 10  4 10  2 10  0  0 12 14 14  4 12 14  4 10  2  0
 0  0  0  8  0  0  8  8  0  0  8  0  0  0  8  8  8  8  0  0  0  8  8  8  8  0  0  8  8  8  0  8  8  8  8  0  8  8  8  0
 0  0  0  0  8  0  0  0  8  8  8  8  0  8  0  0  8  8  0  0  8  8  8  8  8  8  8  0  8  8  0  0  0  8  0  8  0  8  8  8
 0  0  0  0  0  8  8  0  0  8  8  8  8  8  0  0  0  0  8  8  0  0  0  8  8  8  8  8  0  8  8  0  0  8  0  0  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+68x^34+334x^35+580x^36+1366x^37+1510x^38+3458x^39+2136x^40+3074x^41+1508x^42+1378x^43+456x^44+314x^45+102x^46+46x^47+27x^48+14x^49+12x^50

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 1.75 seconds.