The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+39x^38+146x^39+288x^40+664x^41+931x^42+1374x^43+1364x^44+1374x^45+905x^46+650x^47+253x^48+132x^49+29x^50+4x^51+12x^52+6x^53+12x^54+2x^56+4x^58+2x^59

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 0.57 seconds.