The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+110x^37+260x^38+666x^39+1058x^40+2496x^41+3701x^42+5398x^43+5402x^44+5516x^45+3628x^46+2514x^47+1055x^48+560x^49+192x^50+114x^51+30x^52+22x^53+22x^54+12x^55+6x^56+3x^58+2x^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 7.82 seconds.