The generator matrix

 1  0  1  1  1  4  1 10  1  1  6  1  1  4  2  1  1  1  1 10  1  2  1  1  1  2 12  1  1  1  1 14 14  0  1 12  1  1  1  1  1  1  8  1
 0  1  1  0 11  1 10  1  5  6  1  7 15  1  1  8  6  7  2  1  1  1  0  3  2  1  4  5 10 11  6  1  1  0 10  1  0 13 11 10  0  7  1 12
 0  0  2  6  4  6 10 10  0  0  8  2  2 10  2  0 12  8 14 12  0  6  6  8 12 12  2 12  6  6  8 14  8  2  0 12 12  2  0  6 10  0 12  2
 0  0  0 12  0  4 12  4  0  0  0  8  4  0  8  4 12  4 12  4  4  4  0  0  8  8 12 12  8  4  8  8 12  0 12  4 12  8  0 12  4  4  0  4
 0  0  0  0  8  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  0  8  0  8  0  0  8  8  8  8  0  0  0  8  8  0
 0  0  0  0  0  8  0  8  0  0  0  0  0  8  8  0  0  0  8  0  8  8  0  8  0  8  0  0  8  0  8  0  8  8  8  8  0  8  8  0  8  0  0  0
 0  0  0  0  0  0  8  8  8  8  8  8  0  0  8  0  8  8  8  8  8  8  0  0  0  8  8  0  8  8  0  0  8  8  0  0  8  8  0  0  0  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+95x^36+214x^37+539x^38+1260x^39+2345x^40+4408x^41+7586x^42+10546x^43+11517x^44+10396x^45+7941x^46+4614x^47+2074x^48+1068x^49+535x^50+206x^51+88x^52+38x^53+36x^54+14x^55+8x^56+4x^57+3x^58

The gray image is a code over GF(2) with n=352, k=16 and d=144.
This code was found by Heurico 1.16 in 29.3 seconds.