The generator matrix

 1  0  0  1  1  1 10  2  1  1  1 14  1  8  1  1  0 14  1  1  6  1  4 10  1  1  1 12  1  2 12  1 10  1 10  4  0  1  4  1  4 10  1  4
 0  1  0  8  5 13  1  1 14 11 12 12  3  1  6  9  6  1  2  5  1  3  1  2 10  8 15  1  6  6  1 15  0 13  1  8  1  4 14  4  2  1  0  1
 0  0  1 11  3  8 15  2 15  7  2  1 10 13 13 14  1 12  4  9  9 12 11  1  2  1 13 10 11  1  9  9  1 12 11  1  4  6  1  0  1 13  5  0

generates a code of length 44 over Z16 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+420x^41+786x^42+794x^43+645x^44+468x^45+399x^46+234x^47+152x^48+136x^49+29x^50+24x^51+2x^52+4x^53+2x^54

The gray image is a code over GF(2) with n=352, k=12 and d=164.
This code was found by Heurico 1.16 in 0.133 seconds.