The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  1  1
 0 12  0  4  0  0  4 12  0  0  4 12  0  0  4  8 12  8  8 12  8  4  8 12  8  4  8  8 12  4  8  8 12  4  4  4 12  4  0  8
 0  0 12  4  0 12  4  0  8  4 12  8  8  4 12  4  8  4  8 12  4  8  8 12  4  8  0 12  4  0  0 12  4  0  4 12  0  0  0  8
 0  0  0  8  8  8  0  8  8  8  8  8  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0  0  0  0  8  0  8  0  8  0  8

generates a code of length 40 over Z16 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+90x^38+331x^40+84x^42+3x^44+2x^46+1x^68

The gray image is a code over GF(2) with n=320, k=9 and d=152.
This code was found by Heurico 1.16 in 0.0594 seconds.