The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+19x^42+54x^43+136x^44+270x^45+485x^46+1020x^47+1643x^48+3546x^49+4675x^50+7472x^51+8335x^52+9980x^53+8491x^54+7768x^55+4791x^56+3348x^57+1554x^58+1030x^59+399x^60+246x^61+108x^62+60x^63+44x^64+18x^65+23x^66+4x^67+9x^68+3x^70+1x^72+1x^74+1x^76+1x^78

The gray image is a code over GF(2) with n=424, k=16 and d=168.
This code was found by Heurico 1.16 in 38 seconds.