The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+118x^34+180x^35+632x^36+1076x^37+2030x^38+2572x^39+3221x^40+2616x^41+2054x^42+1052x^43+451x^44+180x^45+122x^46+4x^47+38x^48+28x^50+9x^52

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 2.1 seconds.