The generator matrix

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

generates a code of length 40 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+46x^30+137x^32+88x^34+120x^36+80x^38+512x^39+6224x^40+512x^41+88x^42+88x^44+161x^46+70x^48+48x^50+16x^52+1x^78

The gray image is a code over GF(2) with n=320, k=13 and d=120.
This code was found by Heurico 1.16 in 33.2 seconds.