The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+81x^42+12x^43+357x^44+176x^45+594x^46+880x^47+1566x^48+2616x^49+3432x^50+4480x^51+4467x^52+4504x^53+3329x^54+2696x^55+1497x^56+872x^57+633x^58+116x^59+256x^60+24x^61+108x^62+8x^63+39x^64+14x^66+7x^68+1x^70+1x^72+1x^76

The gray image is a code over GF(2) with n=416, k=15 and d=168.
This code was found by Heurico 1.16 in 17 seconds.