The generator matrix

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

generates a code of length 40 over Z16 who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+480x^35+1494x^36+2524x^37+3718x^38+5498x^39+5309x^40+5538x^41+4192x^42+2300x^43+977x^44+440x^45+150x^46+106x^47+26x^48+10x^49+4x^50+1x^52

The gray image is a code over GF(2) with n=320, k=15 and d=140.
This code was found by Heurico 1.16 in 48.9 seconds.