The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+31x^36+6x^37+116x^38+130x^39+277x^40+548x^41+1149x^42+2364x^43+3805x^44+5152x^45+5679x^46+5136x^47+3775x^48+2364x^49+1150x^50+548x^51+249x^52+122x^53+74x^54+14x^55+43x^56+17x^58+11x^60+3x^62+4x^66

The gray image is a code over GF(2) with n=368, k=15 and d=144.
This code was found by Heurico 1.16 in 8.1 seconds.