The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  8  2  8  2  4  1  1  1  2  0  2  2  2  1  1  0  2  2  2  4  2
 0  2  0  0  0  2  6 14  8  8 14  6 12 10  8 14  6 12 14  4  2 10  0  2  2  2 14  2  6 12  6  8 12 14  2 14 10 10 12  2  4 10 12  0
 0  0  2  0  2  2 10  0 12 14  8  2 12 12  2 10  6 14  4 12 10  4  4  4  2  6  2 14  0  8 14  2  8 14  0 14 12 12  2 14 14  8  2 14
 0  0  0  2  2  8 10  2  4  0 14 12  2  0  6  8  6  8  4  4  6  2  6  6 14  4  0  8 12  0  4  0  2  4 12  6  4 14  2 10  2 14  4  4
 0  0  0  0  8  8  0  8  8  8  0  0  8  8  0  0  8  0  8  0  0  8  0  0  8  8  0  8  0  8  0  0  8  0  0  0  8  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+343x^38+288x^39+1153x^40+808x^41+2661x^42+1472x^43+3113x^44+1536x^45+2537x^46+708x^47+1012x^48+248x^49+357x^50+56x^51+59x^52+20x^54+4x^55+6x^56+2x^58

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 26.3 seconds.