The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+59x^38+80x^39+394x^40+624x^41+827x^42+1472x^43+1309x^44+1472x^45+844x^46+624x^47+321x^48+80x^49+50x^50+18x^52+7x^54+4x^56+3x^58+1x^60+2x^62

The gray image is a code over GF(2) with n=352, k=13 and d=152.
This code was found by Heurico 1.16 in 0.742 seconds.