The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  0  1  1  2  1  2  1  8  1  1  2  1  2 12  1  1  0  1  8  2  1  0  2  1  2  1
 0  2  0  6  4  6 12  2  6 14  8 12  0  2  4 10 14  2  2 12 14  2  4  6  6  2  0  2 10  4 10  2  6  0  2  2  4  2 14  2  8  4  4  0
 0  0 12  0  4  0  0  8  4 12  0  4  4 12  8  4  8  0 12  4 12  0  8  8 12  4  8  8  0  0  0  8  8  4  0 12  4  4 12  0  4  0  4  0
 0  0  0 12  0  0  0 12  4  8 12 12  4  8 12  4  4 12 12 12  8 12  4  0 12  0  8  4  0  8  8  0 12  0  8  4  0  0  8  0  4  4  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  0  0  8  8  0  8  0  8  8  0  8  0  8  0  8  0  0  8  8  0  8  8  0  8  0  8  8  0  0  0
 0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  8  0  8  0  0  0  8  0  0  8  8  0  0  0  8  0  8  8  8  0  0  0  8  0  8  0  0  8  8
 0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  0  8  8  8  8  0  8  8  0  0  8  8  8  0  8  0  8  0  0  0  8  0  0  8  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+61x^36+110x^37+214x^38+346x^39+836x^40+946x^41+2340x^42+1688x^43+3434x^44+1708x^45+2258x^46+916x^47+789x^48+284x^49+206x^50+104x^51+57x^52+22x^53+32x^54+18x^55+6x^56+2x^57+6x^58

The gray image is a code over GF(2) with n=352, k=14 and d=144.
This code was found by Heurico 1.16 in 3.5 seconds.