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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+110x^46+8x^47+295x^48+100x^49+321x^50+100x^51+769x^52+1348x^53+2226x^54+1252x^55+750x^56+204x^57+275x^58+44x^59+179x^60+12x^61+107x^62+4x^63+45x^64+32x^66+7x^68+1x^70+1x^72+1x^84

The gray image is a code over GF(2) with n=432, k=13 and d=184.
This code was found by Heurico 1.16 in 1.56 seconds.