The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+34x^42+173x^44+509x^46+1163x^48+512x^49+2540x^50+1536x^51+3502x^52+1536x^53+2531x^54+512x^55+1132x^56+488x^58+141x^60+31x^62+22x^64+8x^66+8x^68+1x^70+2x^72+2x^74

The gray image is a code over GF(2) with n=416, k=14 and d=168.
This code was found by Heurico 1.16 in 4.38 seconds.