The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  1  2  4  1  1  1  1  2  1  2  1  2  1  1  1  2  4  4  1  1
 0 12  0  0  0  4 12  4  0  8  4 12  0  8 12  0  4  8  4 12 12  0  8  8  8  4  0  4  8 12  8  8  8 12 12  4 12  8 12  8 12  4  8 12  0  0
 0  0 12  0  4  4 12  0  0  0  4  8  4  4  0  8  4 12  0  8 12  8  4 12  0 12  8  8  4  8  4  8  4  0  8  0  0  4 12  0  8  8 12 12 12  0
 0  0  0 12  4  0 12  4  0  4 12  8 12  0  4  8  0 12 12  0  8 12  0 12  4  8  0  4  8  0  4 12 12  8  8 12  4  0  0  0  0  4 12 12 12  0
 0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  0  0  8  8  0  8  0  8  8  0  0  0  8  0  8  8  8  0  8  8  8  0  0  0  8  0  8  0  0  8  0
 0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  8  8  0  8  0  8  0  0  8  8  8  0  0  8  0  8  8  0  0  8  8  0  0  8  0  8  0  8  8  8  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  8  0  8  0  8  0  8  8  0  0  8  0  8  8  0  0  0  8  8  0  8  8  8  0  8  8  8  0  8  0
 0  0  0  0  0  0  0  8  8  8  0  8  0  0  0  0  8  8  0  8  0  8  8  0  0  0  0  8  8  8  0  8  8  0  0  8  0  8  0  8  8  0  0  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+92x^37+108x^38+156x^39+244x^40+330x^41+459x^42+662x^43+1519x^44+2912x^45+3495x^46+2736x^47+1524x^48+780x^49+437x^50+244x^51+220x^52+212x^53+92x^54+36x^55+38x^56+26x^57+15x^58+6x^59+5x^60+1x^62+1x^64+1x^66+1x^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 4.58 seconds.