The generator matrix

 1  0  1  1  1  6  1  1 12  1 10  1  1  1  1  6  1  1  0  1  1 12  1  1 10  1  1  1  1  1  1  1  1  1  2  1  1  6 10  1  1  1  6  0
 0  1  3  6  5  1 12 15  1 10  1  9  3  5  0  1 15  6  1  9 12  1  3 10  1  5  9 13 15  3  5 15  5 13  6 11  0  1  1  0 15  6  1  2
 0  0  8  0  0  0  0  8  0  0  0  8  8  8  0  0  8  0  0  8  0  0  8  0  0  8  8  0  0  0  8  0  8  0  8  8  8  8  8  8  0  8  8  8
 0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0  8  0  0  0  0  8  0  8  8  8  0  0  0  8  8  0  0  8  8  8  8  0  0  8  0  8  0  0
 0  0  0  0  8  0  0  8  0  8  8  0  8  0  8  8  8  8  8  8  8  8  0  0  0  8  0  0  0  0  8  8  8  8  8  0  0  8  0  8  8  0  8  8
 0  0  0  0  0  8  8  0  0  8  8  0  0  8  0  0  8  8  8  8  0  0  8  8  8  8  0  0  8  0  0  8  0  0  8  8  8  0  0  8  0  0  8  8

generates a code of length 44 over Z16 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+58x^39+172x^40+366x^41+439x^42+682x^43+688x^44+662x^45+492x^46+334x^47+95x^48+58x^49+25x^50+14x^51+4x^52+2x^53+1x^54+3x^62

The gray image is a code over GF(2) with n=352, k=12 and d=156.
This code was found by Heurico 1.16 in 0.218 seconds.