The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+59x^42+128x^43+348x^44+578x^45+1007x^46+1308x^47+2542x^48+2862x^49+5231x^50+4618x^51+5337x^52+2946x^53+2600x^54+1206x^55+877x^56+478x^57+294x^58+150x^59+103x^60+44x^61+20x^62+14x^63+8x^64+4x^65+4x^66+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 14 seconds.