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  1  1  1  1  1  1  1  1  1  1  2  1  1  4  4  4  2  4  1  2  8  2  4  2  8  4  4  1  1  1
 0 12  0  0  0  0  0  0  0 12 12  4  4  4  4  4  0 12  4  8  0  8  0  4  8  4  4 12 12  0  8 12  4  8 12  0  4  4 12  8  0  8  8  4  4  8 12  0  4 12  0  0  0
 0  0 12  0  0  0  4 12  4  4 12  8  4  8  8  4  0  4 12 12  4  8  8 12  8  0  8  4  0 12  8  0  4  4  0  8  8  8  4  8 12  0 12  8 12  0  0  0  0  4  4 12  0
 0  0  0 12  0  4  4 12  0  8 12 12 12 12  8  0 12  0  4  0  0  4  8 12  4  8  4  0 12  8  8  0  0 12  8 12  4  0  8  4  0  0  0 12  4  0  4  4 12  0 12 12  0
 0  0  0  0 12  4  0 12  4 12  8  4 12  8 12  0  4  4  0 12  0  0  8 12  0 12  0  8 12  8 12  8  4  4  4  0  0 12  4 12  0  4  4  0 12  4  4  4  8 12  8  8  0
 0  0  0  0  0  8  0  0  8  8  0  8  0  0  8  8  0  0  0  0  8  8  0  8  0  8  8  8  8  0  8  8  0  8  0  0  0  0  0  0  8  8  0  8  8  0  0  8  0  0  8  0  0
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  8  8  0  8  0  0  0  0  8  8  8  0  0  0  0  0  8  8  8  8  0  8  0  8  8  0  8  8  0  0  8  8  8  8  0  8  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  0  8  0  0  8  8  8  0  8  8  8  0  0  0  0  0  0  8  8  8  0  0  8  0  8  8  0  0  8  8  8  0  0  8  8  0  8  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+71x^42+102x^43+214x^44+254x^45+437x^46+484x^47+1041x^48+926x^49+2911x^50+2524x^51+5520x^52+3704x^53+5634x^54+2518x^55+2995x^56+1024x^57+970x^58+410x^59+378x^60+202x^61+190x^62+100x^63+74x^64+34x^65+23x^66+4x^67+16x^68+2x^70+2x^71+1x^72+1x^74+1x^78

The gray image is a code over GF(2) with n=424, k=15 and d=168.
This code was found by Heurico 1.16 in 20.8 seconds.