The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+82x^37+238x^38+700x^39+1237x^40+2340x^41+3797x^42+4996x^43+5841x^44+5242x^45+3922x^46+2366x^47+1058x^48+486x^49+219x^50+136x^51+52x^52+20x^53+14x^54+10x^55+2x^56+6x^57+2x^58+1x^60

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 8 seconds.