The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+223x^38+1274x^39+3072x^40+5034x^41+7740x^42+10304x^43+10687x^44+9756x^45+8017x^46+5158x^47+2611x^48+1098x^49+348x^50+124x^51+59x^52+16x^53+6x^54+4x^55+2x^56+2x^58

The gray image is a code over GF(2) with n=352, k=16 and d=152.
This code was found by Heurico 1.16 in 24.5 seconds.