The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+30x^42+44x^43+158x^44+176x^45+403x^46+538x^47+979x^48+1542x^49+2688x^50+3456x^51+3910x^52+4788x^53+3965x^54+3640x^55+2755x^56+1488x^57+962x^58+464x^59+326x^60+188x^61+121x^62+46x^63+52x^64+10x^65+16x^66+4x^67+6x^68+7x^70+5x^72

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 16.4 seconds.