The generator matrix

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

generates a code of length 40 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+146x^36+414x^37+446x^38+800x^39+603x^40+800x^41+380x^42+280x^43+103x^44+58x^45+32x^46+16x^47+10x^48+6x^50+1x^52

The gray image is a code over GF(2) with n=320, k=12 and d=144.
This code was found by Heurico 1.16 in 0.149 seconds.