The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+192x^36+272x^37+612x^38+752x^39+460x^40+752x^41+600x^42+272x^43+168x^44+4x^46+1x^48+8x^52+2x^56

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 0.146 seconds.