The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+386x^36+64x^37+662x^38+448x^39+1104x^40+448x^41+544x^42+64x^43+266x^44+70x^46+34x^48+4x^50+1x^64

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 64.4 seconds.