The generator matrix

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

generates a code of length 50 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+29x^42+60x^43+111x^44+308x^45+619x^46+1308x^47+1819x^48+2676x^49+2564x^50+2676x^51+1806x^52+1308x^53+597x^54+308x^55+83x^56+60x^57+21x^58+11x^60+5x^62+8x^64+2x^66+3x^70+1x^72

The gray image is a code over GF(2) with n=400, k=14 and d=168.
This code was found by Heurico 1.16 in 2.58 seconds.