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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+42x^45+106x^46+104x^47+167x^48+180x^49+428x^50+720x^51+700x^52+688x^53+394x^54+168x^55+139x^56+92x^57+72x^58+32x^59+12x^60+22x^61+20x^62+4x^64+3x^66+1x^72+1x^82

The gray image is a code over GF(2) with n=416, k=12 and d=180.
This code was found by Heurico 1.16 in 17.5 seconds.