The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  2  1  1  1  4  1  0  1  1  1  1  1  4  2  1  4  1  4  2  4  4
 0 12  0 12  0 12  0 12  0  4  8  0 12 12  4  0  8  0  8  0 12 12  0 12 12 12  0 12  8  4 12  4  0  4 12 12 12  4 12  4  0 12 12  8
 0  0  8  0  0  0  0  0  0  0  8  8  0  8  8  0  8  0  8  8  0  0  8  8  0  0  0  0  8  8  8  8  8  8  0  0  8  8  8  0  0  0  8  0
 0  0  0  8  0  0  0  0  0  8  0  0  0  8  8  0  0  8  8  8  0  8  8  0  8  0  0  8  8  0  8  0  8  8  8  0  0  0  0  8  0  0  8  0
 0  0  0  0  8  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  0  8  0  8  8  8  8  8  8  0  0  0  8  8  8  0  8  8  8  0  8  0  8  8
 0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  0  0  0  0  8  0  8  8  0  8  0  8  8  0  8  8  0  8  0  8  0  8  8  8  0  0  8
 0  0  0  0  0  0  8  0  0  0  0  8  0  0  0  8  8  8  8  0  8  0  8  0  8  8  0  0  0  8  8  8  8  0  0  0  0  8  8  8  8  0  8  8
 0  0  0  0  0  0  0  8  0  8  0  0  8  8  0  8  8  8  0  0  8  8  0  8  0  0  0  0  0  0  8  8  8  8  0  0  8  8  8  0  8  0  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  8  0  8  8  8  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  8  0  0  8  8  0  0  0  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+154x^36+16x^37+130x^38+112x^39+442x^40+336x^41+784x^42+1584x^43+1138x^44+1584x^45+740x^46+336x^47+422x^48+112x^49+128x^50+16x^51+110x^52+10x^54+30x^56+6x^60+1x^64

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 1.53 seconds.