The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  2  1  1  2  2  2  4  1  2  1  2  4  2  2  4  8  0  2  4  8  4  4
 0  8  0  8  0  8  0  8  0  8  0  8  0  8  8  0  8  8  0  8  0  8  0  8  0  8  8  0  8  8  0  0  8  8  0  0  0  8  0

generates a code of length 39 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+27x^40+4x^42

The gray image is a code over GF(2) with n=312, k=5 and d=160.
This code was found by Heurico 1.16 in 0.025 seconds.