The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+126x^37+474x^38+1104x^39+2882x^40+4250x^41+8146x^42+9266x^43+12806x^44+9640x^45+8328x^46+4174x^47+2691x^48+908x^49+447x^50+174x^51+42x^52+50x^53+9x^54+2x^55+10x^56+2x^57+3x^58+1x^62

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 23.8 seconds.