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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+112x^51+46x^52+64x^53+32x^54+160x^55+44x^56+48x^59+2x^60+1x^64+2x^72

The gray image is a code over GF(2) with n=432, k=9 and d=204.
This code was found by Heurico 1.16 in 6.5 seconds.