The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  8  2  2  4  1 12  2  0  2  1  8  1  2  2  1  1  2  1  8  1
 0  2  0  0  0  2  6 14  0  8  0  0  6 10  6 12 14  8  2  4 10 10 10 12  2  4 10  2  4  2 14  4 12 14  2  4  6  8 14  6 14  8  8 10
 0  0  2  0  2  2  2  0  4 14  8 14 10  8 14  2 12 12 10  6  8  2  8  4 12  6  6 14 10  4  0  2  2  4  0  0  6  8  2 10  2  0  2  4
 0  0  0  2  2  0  2 10  8  2 14  4  4  2 14  6  0 10  2  8  6  4  0 12  8  4  8 10 10 10  2  2 10  8  4  0  6 10  8  8  4 12 12  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  8  8  8  0  8  8  8  8  8  0  8  8  8  0  0  0  8  0
 0  0  0  0  0  8  0  8  8  8  8  8  0  0  8  0  0  0  8  8  0  0  8  0  0  0  0  8  8  0  8  0  8  8  8  0  0  0  8  8  0  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+238x^37+405x^38+1172x^39+1149x^40+2368x^41+3220x^42+5538x^43+4722x^44+5270x^45+3395x^46+2550x^47+1097x^48+974x^49+252x^50+270x^51+70x^52+44x^53+23x^54+6x^55+1x^56+2x^57+1x^62

The gray image is a code over GF(2) with n=352, k=15 and d=148.
This code was found by Heurico 1.16 in 28 seconds.