The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+91x^38+578x^39+1422x^40+2682x^41+3930x^42+5218x^43+5161x^44+5320x^45+3810x^46+2448x^47+1170x^48+554x^49+242x^50+74x^51+35x^52+20x^53+7x^54+2x^55+3x^56

The gray image is a code over GF(2) with n=352, k=15 and d=152.
This code was found by Heurico 1.16 in 7.05 seconds.