The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+40x^34+140x^35+218x^36+866x^37+730x^38+1588x^39+1118x^40+1572x^41+726x^42+772x^43+184x^44+148x^45+32x^46+28x^47+11x^48+4x^49+6x^50+2x^52+2x^53+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 0.491 seconds.