The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  0  1  1  1  2  1  2  2  1  8  4  1  1  0  1  1  0  4  4  1  2  1  8  1  1  1
 0  2  0  2  0  0 14 14  4  6  2  4  8 10  8  2  2  4  8 10  2  8  4  8 10  6  6 14  4  8  2 10 14  2  8  0  2  2  2 12 14 14  2  6  6  4
 0  0  2  2 12  6  6  4  4  0  6 10 14  2 12  4  6  2  2  4  4 14  0 10  0 14  6  6  4  2 10 12 10  8  6  8  8  0  8  0 10  4  4  6  0  2
 0  0  0  4  0  0  4  8  0  0 12  8  0  4  8  8  4  8  8  4 12 12  4 12  8  8  8  4 12 12  0  4 12  0 12 12  0 12  4  4  4 12  0  8  4  0
 0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  8  8  0  0  8  8  0  0  0  0  8  8  0  8  0  8  0  8  8  8  8  8  0  8  0  0  0  0  0  8
 0  0  0  0  0  8  8  8  8  8  0  8  0  8  8  0  8  0  0  0  8  8  0  0  8  0  0  8  8  8  8  8  8  8  0  8  0  0  0  0  8  0  0  8  0  8

generates a code of length 46 over Z16 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+68x^39+334x^40+504x^41+684x^42+1022x^43+1987x^44+1706x^45+3816x^46+1854x^47+1871x^48+1000x^49+696x^50+360x^51+271x^52+106x^53+48x^54+18x^55+13x^56+12x^57+4x^58+6x^59+2x^60+1x^64

The gray image is a code over GF(2) with n=368, k=14 and d=156.
This code was found by Heurico 1.16 in 3.39 seconds.