The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+157x^36+36x^37+268x^38+368x^39+1276x^40+2512x^41+3444x^42+5808x^43+5107x^44+5752x^45+3452x^46+2512x^47+1238x^48+400x^49+252x^50+16x^51+119x^52+4x^53+8x^54+28x^56+9x^60+1x^64

The gray image is a code over GF(2) with n=352, k=15 and d=144.
This code was found by Heurico 1.16 in 90.7 seconds.