The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  2  1  4  0  4  1  1  1  1  2  2  2
 0 12  0  4  0  0  4  4  8  8  4 12  0  0 12 12 12  8  0 12  8 12  8  8  4  0  0  0  4  4 12  4  4  4  4  4  4  4 12  8
 0  0 12  4  0 12 12  0  8  4  4  0  8 12 12  8 12  0  4  0 12  0 12 12  8  8  8  0 12  8  8  8 12 12 12 12  8  4  0  4
 0  0  0  8  0  0  8  0  0  0  0  8  8  8  8  8  8  0  8  0  8  8  0  8  8  8  8  8  8  8  0  0  8  0  0  0  0  0  8  8
 0  0  0  0  8  0  0  0  0  8  8  8  0  0  8  0  8  8  8  8  0  8  8  8  0  0  8  8  8  8  8  0  0  0  8  0  8  0  0  8
 0  0  0  0  0  8  8  8  8  8  8  0  8  0  0  0  8  8  8  8  8  8  0  0  8  0  8  0  0  8  8  0  8  0  0  8  0  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+60x^35+90x^36+100x^37+216x^38+360x^39+422x^40+360x^41+224x^42+84x^43+54x^44+52x^45+8x^46+8x^51+8x^52+1x^64

The gray image is a code over GF(2) with n=320, k=11 and d=140.
This code was found by Heurico 1.16 in 6.68 seconds.