The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  0  1  1  6  1  1 12  1  1 10  1  1  1  1  0  1  6  1 10  1  1  1  1  1  1  1  6  1 10  1  6  1  1  1  0  6  1  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  1  0  5  1  6  3  1 12 15  1 10  9  0  3  1  5  1  6  1 12 10 15  3 15  0  0  1  6  1  9  1  5 12  9  1  1  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0  8  8  8  0  8  0  8  8  0  0  8  0  0  8  0  0  8  0  8  0  8  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  8  8  0  8  0  8  0  8  8  8  8  8  8  8  8  8  0  8  0  0  0  0  8  8  0  0  8  8  8  8  0  8  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  8  8  8  8  0  0  0  0  8  8  8  0  0  0  8  0  0  8  8  8  8  8  8  8  0  0  8  0  8  0  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  8  0  0  0  8  0  0  8  8  0  8  0  8  0  0  0  8  8  0  8  0  8  0  8  8  8  0  8  8  8  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  8  8  0  0  8  8  0  0  8  0  0  8  0  8  0  0  8  8  8  8  0  0  0  8  8  0  0  8  0  8  8  8  0  0  8  0  8  8  8  8  0  0
 0  0  0  0  0  0  0  8  0  8  0  0  0  0  0  0  8  8  8  8  0  0  8  0  8  8  8  0  0  0  8  8  8  8  0  8  8  0  0  8  0  8  0  8  0  0  8  0  8  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  8  0  0  0  8  8  8  0  8  0  8  0  0  8  8  8  0  0  8  8  0  8  0  0  0  8  8  0  0  8  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+43x^40+12x^41+53x^42+116x^43+98x^44+508x^45+155x^46+2224x^47+561x^48+6648x^49+1152x^50+9656x^51+1150x^52+6648x^53+553x^54+2224x^55+141x^56+508x^57+82x^58+116x^59+46x^60+12x^61+37x^62+6x^64+8x^66+2x^68+7x^70+1x^74

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 9.34 seconds.