The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  1  2  1  1  1  8  1  1  1  2  1  0  1  2  1 12  2  2  1  1  2  1  1  1  2  1
 0  2  0  6  4  6 12  2  8  0  6 14  4  4  2 10  6  2  0 10 14  2 12  2  8  6  0  6  6  2  6 14 12  2  6 10  6 10  6  2  2 10  6  4
 0  0 12  0  4  0  8  0  0  4  4  4  4  0 12 12 12  4  8  4 12  0  8  0  4 12  4  0  8  0  8  8 12  4  4  8  4 12  8  8  8  8  4 12
 0  0  0 12  0  8  8  4  4  4  4  0 12  4  0  4  4  8  0  4  8 12  0 12  8  0 12  8  4  0 12  4 12  4  8  8  4 12  8  0 12  0  4  0
 0  0  0  0  8  8  8  8  0  0  0  8  8  8  0  8  0  8  8  8  0  0  0  8  0  8  8  0  8  8  8  0  0  0  0  0  8  0  8  0  8  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+80x^39+352x^40+272x^41+288x^42+672x^43+819x^44+672x^45+288x^46+272x^47+256x^48+80x^49+28x^52+14x^56+1x^60+1x^64

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 77.1 seconds.