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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+61x^44+64x^45+90x^46+150x^47+125x^48+344x^49+259x^50+1120x^51+1010x^52+1780x^53+1029x^54+1148x^55+251x^56+308x^57+95x^58+112x^59+69x^60+60x^61+45x^62+30x^63+14x^64+4x^65+13x^66+4x^68+3x^70+1x^72+1x^74+1x^78

The gray image is a code over GF(2) with n=424, k=13 and d=176.
This code was found by Heurico 1.16 in 1.43 seconds.