The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  1  1  6  1  1 12 10  1  1  1  0  1  1 10  1 12  1  1  1  6  1  1  1  1  1
 0  1  3  6  5  1 12 15  1  9 10  1  0  3  1  6  5  1 12 15  1  1  9 10  3  1  0  9  1 15  1  6 12  5  1 12 10  0  6 10
 0  0  8  0  0  0  0  0  8  8  0  8  8  8  0  8  8  0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  0  0  0  0  8  0  0  8
 0  0  0  8  0  0  8  0  8  8  8  0  8  8  0  0  0  8  8  0  0  0  0  8  8  8  0  8  8  8  8  8  8  8  8  0  0  0  0  0
 0  0  0  0  8  0  8  8  0  0  8  0  0  8  8  0  8  8  8  8  0  8  0  8  0  8  8  8  0  8  0  0  0  8  0  8  0  0  0  0
 0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  0  8  8  0  8  8  8  0  0  8  0  8  8  0  0  0  0  0  0  8  0  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+257x^36+256x^37+384x^38+768x^39+780x^40+768x^41+384x^42+256x^43+230x^44+1x^48+9x^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 21.8 seconds.