The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+172x^38+224x^39+831x^40+1172x^41+1942x^42+2440x^43+2884x^44+2460x^45+2000x^46+1168x^47+629x^48+204x^49+154x^50+8x^51+56x^52+4x^53+16x^54+15x^56+4x^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 80.6 seconds.