The generator matrix

 1  0  0  0  1  1  1  2 10  1  8  4  1  1  1  1  6  1 12  1  1 10  4  0  0  1  1 14  1  1  0  6  1 10  1  1 10  1  8  1 14  8  1  1
 0  1  0  0  0  9  5  1  1  8  6  1 15  2  3  1  4 14  1  8 13  1  8  1  1  6  9  2 15 13  1 12  2  0  2  6  1  8  1  3  1  1  2  0
 0  0  1  0  1  1  4  5 14 14  1  5 13  7 14 13  1 12  5 10 14  4  1 12 11 11  6  8  3 13  2  1  8  1 10 15  4  4  9  2 13 14 10  0
 0  0  0  1  1  4  1  1  7  5  1  2  5 14  2 15  8 11  4 12  9 12 15  5  9 12  2  1 10  7 10  2 14 10  1  2 15  9  6  9  5  2 15  0
 0  0  0  0 12  0  0  0  0  0  0  0  8  8  8  8  8  0  4  4  4  4 12  4 12  8 12 12  4 12  4  0 12  4  0  4  8  4 12  8  4  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+90x^36+772x^37+2043x^38+5604x^39+9831x^40+20014x^41+29158x^42+41292x^43+43027x^44+43008x^45+29744x^46+20108x^47+9434x^48+5100x^49+1770x^50+692x^51+303x^52+92x^53+37x^54+16x^55+2x^56+6x^57

The gray image is a code over GF(2) with n=352, k=18 and d=144.
This code was found by Heurico 1.16 in 367 seconds.