The generator matrix

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

generates a code of length 46 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+71x^36+62x^37+143x^38+394x^39+387x^40+1568x^41+2354x^42+5282x^43+7288x^44+10036x^45+10319x^46+10156x^47+7199x^48+5384x^49+2368x^50+1500x^51+355x^52+350x^53+142x^54+74x^55+53x^56+8x^57+22x^58+2x^59+6x^60+11x^62+1x^70

The gray image is a code over GF(2) with n=368, k=16 and d=144.
This code was found by Heurico 1.16 in 31.1 seconds.