The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+36x^40+42x^41+102x^42+192x^43+322x^44+492x^45+805x^46+1322x^47+2376x^48+3544x^49+4555x^50+5152x^51+4575x^52+3608x^53+2408x^54+1364x^55+757x^56+458x^57+264x^58+144x^59+108x^60+44x^61+49x^62+18x^63+13x^64+4x^65+7x^66+3x^68+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 15.4 seconds.