The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  1  1  2 12  1  1  2  0  1  1 12  2  1  1  1  2  1  1  1  1  1  1  0  2  0  1  1  1  1  1
 0  2 12  6  0  6 12 10  0  6 12 10  0  6  2  6 10 12 10  2  0  0  6  2  6 12  2 10 12  0 10  6 10 10 10 12  0  8  2  6  2 12  2  4  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  8  0  0  8  0  8  0  8  8  8  8  8  0  8  8  0  0  8  0  8  8  0  8  0  8  8  0  0  0  0  0  0
 0  0  0  8  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  0  0  8  0  0  8  8  8  0  0  0  8  0  0  8  8  8  0  0  8  8  8  8  8  0  0
 0  0  0  0  8  0  0  0  0  0  8  0  8  0  8  8  8  8  0  8  8  0  8  8  0  8  0  0  0  8  8  0  8  8  8  8  8  8  0  0  8  8  0  0  0  0
 0  0  0  0  0  8  0  0  0  8  0  8  0  0  8  0  8  0  0  8  8  8  8  0  8  8  8  0  0  0  8  0  8  0  0  8  0  0  0  8  0  0  8  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  0  0  8  8  0  0  0  0  8  8  0  8  0  8  0  0  0  0  8  0  8  0  8  0  8  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  8  0  8  8  0  0  0  0  0  8  0  0  8  8  8  8  0  8  0  8  0  8  8  8  0  8  8  0  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  8  8  8  8  0  0  0  8  8  8  8  0  0  0  8  0  8  0  8  0  0  8  8  8  8  0  8  0  0  0  0  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+71x^36+20x^37+48x^38+100x^39+272x^40+288x^41+656x^42+640x^43+2873x^44+1000x^45+4480x^46+1000x^47+2865x^48+640x^49+656x^50+288x^51+232x^52+100x^53+48x^54+20x^55+58x^56+21x^60+4x^64+3x^68

The gray image is a code over GF(2) with n=368, k=14 and d=144.
This code was found by Heurico 1.16 in 3.56 seconds.