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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+134x^44+4x^45+267x^46+40x^47+345x^48+236x^49+927x^50+1264x^51+1837x^52+1244x^53+895x^54+232x^55+336x^56+52x^57+207x^58+114x^60+36x^62+10x^64+2x^66+6x^68+2x^70+1x^84

The gray image is a code over GF(2) with n=416, k=13 and d=176.
This code was found by Heurico 1.16 in 1.38 seconds.