The generator matrix

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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+35x^42+133x^44+233x^46+425x^48+807x^50+2482x^52+2048x^53+4045x^54+2048x^55+2591x^56+752x^58+385x^60+208x^62+99x^64+51x^66+24x^68+9x^70+3x^72+3x^74+1x^78+1x^80

The gray image is a code over GF(2) with n=432, k=14 and d=168.
This code was found by Heurico 1.16 in 6.12 seconds.