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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+48x^44+132x^45+257x^46+384x^47+625x^48+1024x^49+1429x^50+2386x^51+3483x^52+4308x^53+4650x^54+4232x^55+3576x^56+2432x^57+1515x^58+984x^59+470x^60+320x^61+212x^62+128x^63+74x^64+40x^65+32x^66+14x^67+11x^68+1x^70

The gray image is a code over GF(2) with n=432, k=15 and d=176.
This code was found by Heurico 1.16 in 17.3 seconds.