The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+36x^36+44x^37+149x^38+132x^39+283x^40+570x^41+856x^42+1306x^43+1474x^44+1298x^45+886x^46+578x^47+219x^48+126x^49+129x^50+30x^51+24x^52+10x^53+21x^54+2x^55+9x^56+6x^58+2x^60+1x^66

The gray image is a code over GF(2) with n=352, k=13 and d=144.
This code was found by Heurico 1.16 in 0.863 seconds.