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

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

Homogenous weight enumerator: w(x)=1x^0+73x^30+114x^31+185x^32+266x^33+398x^34+556x^35+927x^36+1736x^37+3331x^38+5520x^39+6507x^40+5504x^41+3449x^42+1740x^43+888x^44+612x^45+359x^46+238x^47+176x^48+70x^49+64x^50+24x^51+16x^52+4x^53+5x^54+3x^56+1x^58+1x^68

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 13.6 seconds.