The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+364x^36+120x^37+720x^38+400x^39+1065x^40+384x^41+552x^42+112x^43+236x^44+8x^45+104x^46+26x^48+3x^52+1x^60

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 4.04 seconds.