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

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

Homogenous weight enumerator: w(x)=1x^0+206x^37+525x^38+860x^39+1233x^40+2072x^41+3277x^42+5112x^43+6243x^44+5016x^45+3543x^46+2086x^47+1034x^48+766x^49+417x^50+228x^51+92x^52+30x^53+12x^54+2x^55+4x^56+6x^57+2x^58+1x^68

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 14.1 seconds.