The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+142x^35+598x^36+1470x^37+2093x^38+2826x^39+2513x^40+2708x^41+1767x^42+1312x^43+600x^44+220x^45+95x^46+22x^47+8x^48+5x^50+2x^51+2x^53

The gray image is a code over GF(2) with n=320, k=14 and d=140.
This code was found by Heurico 1.16 in 1.56 seconds.