The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  2  0  1  1  0  1 12  2  1  4  1  2  0  1  1  1  1  1 12  8  8  2
 0  2  0  6  4  6 12  2  8  0  6 14  4  4  2 10  6  2 14  2  0  2  2 10  2 10  4  2  2 14  2  6  0  2  4  0  2  2  2 14
 0  0 12  0  4  0  0  8  0  4  4 12  8  4 12 12  8  0  8  8  0 12  4 12  4  8  8  0  0 12 12  4  0  4  4  8  4  4  8  0
 0  0  0 12  0  0  8  4  4  4  4  8 12  4  0  4  0 12  4  8  0  8  4  4 12  8  4 12  8  0  8  0  8 12  0  0 12  0 12 12
 0  0  0  0  8  8  8  8  0  0  0  8  8  8  0  8  8  8  8  8  8  8  0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+106x^35+198x^36+358x^37+474x^38+708x^39+487x^40+702x^41+442x^42+318x^43+159x^44+84x^45+8x^46+16x^47+16x^48+6x^49+2x^50+4x^51+3x^52+2x^53+2x^54

The gray image is a code over GF(2) with n=320, k=12 and d=140.
This code was found by Heurico 1.16 in 0.458 seconds.