The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+76x^37+903x^38+2350x^39+5942x^40+9540x^41+15494x^42+19868x^43+22383x^44+19972x^45+16263x^46+9772x^47+5287x^48+1896x^49+960x^50+228x^51+83x^52+32x^53+12x^54+6x^55+4x^57

The gray image is a code over GF(2) with n=352, k=17 and d=148.
This code was found by Heurico 1.16 in 92.2 seconds.