The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+70x^37+460x^38+1296x^39+2499x^40+5202x^41+7038x^42+10624x^43+10592x^44+11278x^45+7439x^46+5146x^47+2214x^48+1006x^49+374x^50+156x^51+78x^52+28x^53+15x^54+10x^55+8x^56+2x^58

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 24.2 seconds.