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

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

Homogenous weight enumerator: w(x)=1x^0+155x^44+30x^46+276x^48+112x^50+256x^51+356x^52+768x^53+4316x^54+768x^55+355x^56+256x^57+128x^58+232x^60+22x^62+110x^64+40x^68+9x^72+1x^76+1x^80

The gray image is a code over GF(2) with n=432, k=13 and d=176.
This code was found by Heurico 1.16 in 42.8 seconds.