The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+95x^38+234x^39+851x^40+1044x^41+2091x^42+2286x^43+3239x^44+2438x^45+2021x^46+926x^47+722x^48+176x^49+166x^50+50x^51+18x^52+6x^53+10x^54+8x^55+1x^58+1x^60

The gray image is a code over GF(2) with n=352, k=14 and d=152.
This code was found by Heurico 1.16 in 2.19 seconds.