The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+139x^36+132x^37+574x^38+696x^39+1571x^40+2448x^41+3504x^42+4968x^43+4858x^44+4840x^45+3508x^46+2440x^47+1547x^48+752x^49+464x^50+88x^51+175x^52+20x^53+14x^54+25x^56+4x^60

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 11.5 seconds.