The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+72x^32+12x^33+52x^34+44x^35+381x^36+136x^37+720x^38+624x^39+2836x^40+3640x^41+8690x^42+8792x^43+13416x^44+8944x^45+8704x^46+3680x^47+2813x^48+540x^49+744x^50+156x^51+354x^52+40x^53+32x^54+16x^55+83x^56+2x^58+8x^60+2x^64+1x^68+1x^72

The gray image is a code over GF(2) with n=352, k=16 and d=128.
This code was found by Heurico 1.16 in 26 seconds.