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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+104x^32+171x^36+64x^38+392x^40+1280x^42+4096x^43+1459x^44+192x^46+259x^48+121x^52+43x^56+9x^60+1x^72

The gray image is a code over GF(2) with n=344, k=13 and d=128.
This code was found by Heurico 1.16 in 1.18 seconds.