The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+146x^36+20x^37+150x^38+88x^39+753x^40+1028x^41+2452x^42+4784x^43+7049x^44+11832x^45+9628x^46+10656x^47+7063x^48+5432x^49+2488x^50+848x^51+697x^52+116x^53+126x^54+8x^55+127x^56+4x^57+4x^58+27x^60+8x^64+1x^68

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.