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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+82x^40+102x^41+156x^42+262x^43+372x^44+460x^45+599x^46+1772x^47+1157x^48+5556x^49+1737x^50+8262x^51+1700x^52+5640x^53+1196x^54+1720x^55+645x^56+430x^57+314x^58+242x^59+120x^60+92x^61+75x^62+28x^63+18x^64+8x^65+17x^66+2x^67+2x^70+1x^72

The gray image is a code over GF(2) with n=408, k=15 and d=160.
This code was found by Heurico 1.16 in 19.6 seconds.