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  1  2  1  2  4  4  1  2  1  4  2  8  4  4  0  2  2  4  2  8  2  1
 0 12  0  4  0  0  4 12  0  8  4  0  4  8  4  4  0  8  0  4 12  0 12  0 12  4  8  4  4  0  8  4  8 12  4  4  4  8  0  8 12 12 12  4 12  0
 0  0 12  4  0 12  4  0  0  4  0  8 12 12  8  4  8  4  4  4  0  8  0 12  4  4  8  4 12 12 12  4 12  8  4 12  4  4  4  4  8  8 12  4  0  0
 0  0  0  8  0  0  0  0  0  8  8  8  8  0  0  0  0  0  8  8  0  8  0  8  0  0  0  8  0  8  0  0  8  8  0  8  0  8  8  0  8  0  8  0  8  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  0  8  8  8  0  8  0  8  8  0  8  0  0  8  8  8  8  8  8  8  8  0  0  8  0  0
 0  0  0  0  0  8  0  0  0  8  0  0  0  0  0  8  8  8  8  0  8  8  0  8  8  8  8  0  0  0  8  0  0  8  0  0  8  0  8  8  0  0  8  0  8  0
 0  0  0  0  0  0  8  0  0  8  8  8  0  0  0  0  8  8  0  8  0  8  8  8  8  8  8  0  0  8  8  8  8  0  0  8  0  0  0  0  0  8  0  8  0  8
 0  0  0  0  0  0  0  8  0  0  8  0  0  0  0  8  8  8  8  0  0  8  8  8  8  0  0  8  8  8  0  8  0  8  8  0  0  0  0  0  8  8  0  0  0  0
 0  0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  8  0  0  0  8  8  8  0  0  8  8  8  8  0  0  8  8  8  0  0  0  8  0  8  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+37x^36+76x^37+111x^38+236x^39+236x^40+572x^41+557x^42+1550x^43+1293x^44+2692x^45+1713x^46+2652x^47+1281x^48+1572x^49+566x^50+624x^51+173x^52+192x^53+101x^54+56x^55+42x^56+16x^57+21x^58+2x^59+7x^60+3x^62+2x^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 4.65 seconds.