The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+163x^38+216x^39+690x^40+1248x^41+1699x^42+2864x^43+2643x^44+2928x^45+1699x^46+1256x^47+609x^48+176x^49+89x^50+16x^51+48x^52+26x^54+8x^56+4x^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 7.19 seconds.