The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+114x^39+226x^40+530x^41+466x^42+1274x^43+1328x^44+3106x^45+2056x^46+3494x^47+1481x^48+1102x^49+384x^50+446x^51+142x^52+118x^53+32x^54+48x^55+19x^56+8x^57+6x^58+2x^60+1x^72

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 19.4 seconds.