The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+62x^37+224x^38+494x^39+830x^40+1202x^41+1722x^42+2334x^43+2667x^44+2438x^45+1776x^46+1168x^47+701x^48+348x^49+207x^50+104x^51+53x^52+24x^53+6x^54+10x^55+2x^56+6x^57+1x^58+2x^59+2x^60

The gray image is a code over GF(2) with n=352, k=14 and d=148.
This code was found by Heurico 1.16 in 3.13 seconds.