The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  8  1  1  2  0  1  1  1  1  2 12  4  1  1  8  1  1  0  2  4  2  2  0  4  2  8  1
 0  2  0 14  4  6 12  2  0  6 14 12  6  2  8  2 14  2 14 10  0 10 10  2  2  4  6  2  4  6  2  2  2  8 14  0  4  8  2  0
 0  0 12  4  4  0  0  4  0  0  4  8  0  4  4  4  4  8  4  0  0  0  8  8  4 12  0  4 12  4  0 12  4  4 12  4 12  4 12  0
 0  0  0  8  0  0  0  0  0  0  8  0  0  0  0  8  0  0  8  0  8  0  8  8  0  8  8  8  0  8  0  8  8  0  8  0  0  8  8  0
 0  0  0  0  8  0  0  0  0  8  8  8  8  0  8  8  8  8  0  8  0  0  8  0  8  8  0  8  0  0  8  8  0  8  8  0  0  8  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  0  0  8  0  8  8  8  0  8  0  8  0  8  0  0  0  8  8  0  8  8  8  0  8  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  0  0  0  8  8  0  0  8  0  8  0  8  0  8  0  8  8  0  8  8  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  0  8  8  0  8  8  0  0  0  8  8  8  0  8  8  0  8  8  8  8  8  0  8
 0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  0  0  8  0  8  0  8  8  8  8  0  0  8  0  0  0  0  8  8  0  8  0  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+34x^30+42x^31+130x^32+148x^33+510x^34+684x^35+1572x^36+2138x^37+4147x^38+4116x^39+5695x^40+4216x^41+4038x^42+2168x^43+1685x^44+628x^45+448x^46+146x^47+117x^48+36x^49+34x^50+12x^51+14x^52+2x^53+3x^54+1x^56+2x^58+1x^60

The gray image is a code over GF(2) with n=320, k=15 and d=120.
This code was found by Heurico 1.16 in 10.5 seconds.