The generator matrix

 1  0  1  1  1  6  1  1  8  1 14  1  1 12  1  1  1  2  1  1  6  8  1  1  1  1  4  1  6 14  1  0  1  1  1  6  1  1  1 10  1 14  1  1  6  6  1  8  1  1  1
 0  1 11  6 13  1  0  3  1  6  1  5  2  1 11 13  0  1  6  7  1  1  8 10  3  9  1  1  1  1 10  1  4  9  9  1  4  0 14  1 15  1  8  7  1  1 10  4 13  8  0
 0  0 12  0  4  0  0  4  8  0  8  4  0  0  8  0  4  8 12 12  4 12 12  0  0  4  8  4  4  4  8  4  4  8  0  8  4  8  0  4  0  4 12  0  8  8 12  0  0 12  0
 0  0  0 12  0  0 12  4 12  8  4  4 12  8 12 12 12  4 12  0  4  0  8  8  8  4 12  0 12  8  0  4  8  8  8  8  8  8 12  4  0  4  0 12  0  8  4  4  4  8  0
 0  0  0  0  8  0  0  0  0  0  0  8  0  8  8  8  8  8  0  8  8  0  8  8  0  8  8  8  0  0  0  0  0  0  8  0  8  8  0  0  0  0  0  8  0  0  8  8  0  8  0
 0  0  0  0  0  8  0  0  8  8  8  8  8  8  0  8  0  0  0  0  0  8  8  0  0  8  8  8  8  0  0  0  0  0  0  8  8  8  8  0  8  8  8  0  0  0  8  8  0  0  0
 0  0  0  0  0  0  8  8  8  0  0  8  0  0  8  8  8  0  0  8  8  8  8  8  8  0  8  0  0  8  8  8  8  0  0  8  0  0  8  0  0  8  8  0  0  8  0  8  0  8  0

generates a code of length 51 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+39x^42+56x^43+224x^44+324x^45+696x^46+1294x^47+2567x^48+3522x^49+5266x^50+4920x^51+5140x^52+3688x^53+2494x^54+1208x^55+705x^56+252x^57+176x^58+60x^59+55x^60+20x^61+29x^62+10x^63+11x^64+2x^65+3x^66+4x^67+1x^68+1x^70

The gray image is a code over GF(2) with n=408, k=15 and d=168.
This code was found by Heurico 1.16 in 9.96 seconds.