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

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

Homogenous weight enumerator: w(x)=1x^0+37x^44+80x^45+155x^46+250x^47+201x^48+464x^49+315x^50+1256x^51+1281x^52+3104x^53+2197x^54+3090x^55+1303x^56+1196x^57+287x^58+482x^59+167x^60+184x^61+99x^62+100x^63+65x^64+28x^65+18x^66+6x^67+14x^68+2x^72+1x^76+1x^78

The gray image is a code over GF(2) with n=432, k=14 and d=176.
This code was found by Heurico 1.16 in 5.75 seconds.