The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  6  1  1  0  1  1 12 10  1  1  1  1  1  0  1  1  6  1  1  1  1 12  1 10  1  1  1  6  1 10  1  6  0  4  0  0  0  2
 0  1  3  6  5  1 12  7  1 10  9  1  6  1  3  0  1  5 15  1  1 12  9 10  0  6  1  3 15  1  5  9 12  3  1 10  1  5  0 12  1 15  1  3  1  1  0  1  1  2  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  8  0  8  8  8  0  8  0  0  8  8  8  0  0  0  8  0  8  0  8  8  0  8  0  8  0  0  8  8  8  0  0  8  8  8
 0  0  0  8  0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  0  8  0  8  8  0  8  8  0  0  8  0  0  8  8  0  8  8  0  0  0  0  8  0  8  0  0  8  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  0  8  8  0  8  8  8  0  8  8  8  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  8  8  8  8  0  8  8  0  0  0  0  8  8  0  0  8  0  0  8  8  8  0  8  0  8  0  8  8  0  0  8  8  8  8  0  0
 0  0  0  0  0  0  8  0  0  0  8  0  8  0  8  8  0  0  0  0  8  8  8  0  0  8  0  0  8  8  8  8  0  8  8  8  8  0  8  0  0  8  0  0  8  0  0  0  0  8  8
 0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  0  0  8  8  0  8  0  8  0  8  8  0  8  0  8  8  0  8  0  0  8  0  8  0  8  0  0  8  8  0  0  8  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  8  8  0  0  8  0  8  0  0  8  8  8  8  0  0  8  8  0  0  8  8  8  0  8  8  0  8  8  0  8  0  8  0  8  0  8  8  8
 0  0  0  0  0  0  0  0  0  8  8  0  8  0  8  8  0  8  8  0  8  0  0  8  8  8  0  0  0  8  8  8  8  0  0  0  8  8  0  0  0  0  8  0  0  0  8  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+97x^40+92x^42+72x^43+550x^44+416x^45+1134x^46+3232x^47+3741x^48+9824x^49+6648x^50+13872x^51+6835x^52+9824x^53+3564x^54+3232x^55+1288x^56+416x^57+316x^58+72x^59+220x^60+22x^62+56x^64+11x^68+1x^72

The gray image is a code over GF(2) with n=408, k=16 and d=160.
This code was found by Heurico 1.16 in 35.2 seconds.