The generator matrix

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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+144x^49+168x^50+416x^51+420x^52+662x^53+675x^54+630x^55+372x^56+252x^57+96x^58+108x^59+36x^60+62x^61+20x^62+30x^63+3x^64+1x^86

The gray image is a code over GF(2) with n=432, k=12 and d=196.
This code was found by Heurico 1.16 in 0.404 seconds.