The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+202x^32+96x^34+16x^35+608x^36+128x^37+504x^38+704x^39+1321x^40+6016x^41+1280x^42+10848x^43+1624x^44+6016x^45+944x^46+704x^47+961x^48+128x^49+224x^50+16x^51+312x^52+24x^54+75x^56+16x^60

The gray image is a code over GF(2) with n=344, k=15 and d=128.
This code was found by Heurico 1.16 in 66.9 seconds.