The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+224x^37+553x^38+1502x^39+2296x^40+4510x^41+7148x^42+11020x^43+10737x^44+11462x^45+7197x^46+4568x^47+2275x^48+1216x^49+417x^50+244x^51+74x^52+56x^53+10x^54+10x^55+8x^56+2x^57+3x^58+1x^60+2x^61

The gray image is a code over GF(2) with n=352, k=16 and d=148.
This code was found by Heurico 1.16 in 99.4 seconds.