The generator matrix

 1  0  1  1  1  6  1  1  8  1 14  1  1  1  0  1 14  1  1  1  0  6  1  1  0  1  1  1  1  1 10  1  1  1  1  6  8  1  1  1 10 14  2  8  8 14  1  1  1  1  2
 0  1 11  6  1  1  8 11  1 13  1  6  3  8  1  6  1 13 10  3  1  1  5  0  1  5  1  6  4 14  1 15 15  3 15  1  1  0 10  2  1  1  4  1  2  1 14  7  0  5  8
 0  0 12  0  0  0  0  0  8  4  0  8  0  0  8  8  8  8  0  4 12 12 12  4  4  4  4  4 12  4  4  8 12  8  4  0  8 12  4  0  8  0 12 12  0 12  8  4  8  4  4
 0  0  0 12  0  0 12  8 12  0 12  0  0  0 12 12  8  4 12  0 12  8  8 12  8 12  4  0  8 12  8  8  4 12  4  0  0 12  0  4  4  8  0 12  4  0  4  0 12  8 12
 0  0  0  0  4  0  8  4  0  8  8  0  8  4  4 12  4  0 12 12  0  4  4  8  8  0 12 12  8 12 12  0  0 12 12  0  4  8  4  8  4 12  0  4  0  4  0  0  4  4  4
 0  0  0  0  0  8  8  8  0  8  8  8  0  8  0  8  8  8  0  8  8  8  0  8  8  0  8  0  0  0  0  8  8  0  8  0  8  0  8  0  8  0  0  0  8  0  0  0  8  0  0

generates a code of length 51 over Z16 who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+64x^43+156x^44+396x^45+667x^46+1252x^47+2478x^48+3918x^49+4889x^50+5224x^51+5008x^52+3818x^53+2378x^54+1294x^55+612x^56+278x^57+118x^58+94x^59+52x^60+34x^61+11x^62+6x^63+13x^64+4x^65+1x^66+2x^67

The gray image is a code over GF(2) with n=408, k=15 and d=172.
This code was found by Heurico 1.16 in 10.4 seconds.