The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+147x^32+66x^34+501x^36+630x^38+1940x^40+4924x^42+4096x^43+8087x^44+4096x^45+4972x^46+2055x^48+602x^50+443x^52+62x^54+107x^56+8x^58+25x^60+5x^64+1x^72

The gray image is a code over GF(2) with n=352, k=15 and d=128.
This code was found by Heurico 1.16 in 15.8 seconds.