The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+30x^45+96x^46+72x^47+314x^48+176x^49+624x^50+948x^51+1008x^52+1636x^53+1067x^54+972x^55+639x^56+176x^57+232x^58+44x^59+64x^60+30x^61+19x^62+12x^63+20x^64+8x^66+1x^70+1x^72+1x^78+1x^80

The gray image is a code over GF(2) with n=424, k=13 and d=180.
This code was found by Heurico 1.16 in 1.73 seconds.