The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+24x^45+46x^46+72x^47+102x^48+112x^49+130x^50+696x^51+214x^52+1264x^53+274x^54+696x^55+175x^56+112x^57+38x^58+72x^59+2x^60+24x^61+20x^62+15x^64+4x^70+2x^72+1x^88

The gray image is a code over GF(2) with n=424, k=12 and d=180.
This code was found by Heurico 1.16 in 1.05 seconds.