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

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

Homogenous weight enumerator: w(x)=1x^0+126x^44+4x^45+252x^46+60x^47+483x^48+436x^49+982x^50+1036x^51+1517x^52+1036x^53+986x^54+436x^55+413x^56+60x^57+158x^58+4x^59+119x^60+50x^62+22x^64+4x^66+5x^68+1x^72+1x^76

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 1.49 seconds.