The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+218x^37+687x^38+1492x^39+2520x^40+4600x^41+7358x^42+10036x^43+11574x^44+10078x^45+7563x^46+4848x^47+2440x^48+1208x^49+506x^50+236x^51+92x^52+36x^53+12x^54+12x^55+13x^56+4x^57+2x^58

The gray image is a code over GF(2) with n=352, k=16 and d=148.
This code was found by Heurico 1.16 in 32.1 seconds.