The generator matrix

 1  0  1  1  1  4  1  2  1  1  1 14  8  2  1  1  1  1  0  1  1  1 10  1 14  2  1  1 10  1  8  1  2  1 12  1  1  4  1  1  6  1 12 12  1  2
 0  1  1  0  3  1 15  1  6  5  2  1  1  1  7 14  5 14  1  8 13 11  1 12  1  1 13  6  1  7  1  2 12  1  2  9 14  4 12 14  1 15  1  1  9 12
 0  0  2  6  0  2  6  2  0  8  6 12  4  4 10  4  6  6 14  2  8  8 10 12  8 14  4  0  2  6  6  0  2 10 14  2  4  2 10 14 12  0  2  2  8  2
 0  0  0 12  0  0  8  8  0  0  4  0  0  0  0  8  8  4  0  8 12  4 12  4 12 12  8 12  8  4  4 12  4  4  8  4  8  0 12 12  4  4 12  8  8 12
 0  0  0  0  8  0  0  0  0  8  0  0  8  8  8  8  8  8  8  0  8  0  0  0  8  0  0  8  8  0  8  0  8  8  0  8  8  0  8  8  8  8  0  0  8  0
 0  0  0  0  0  8  8  0  8  8  8  8  8  0  0  8  8  8  0  8  8  8  8  0  0  0  8  0  8  0  8  8  8  0  0  8  0  0  0  8  8  8  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+80x^39+336x^40+626x^41+1561x^42+2228x^43+4196x^44+4490x^45+5808x^46+4668x^47+4211x^48+2006x^49+1396x^50+592x^51+328x^52+126x^53+60x^54+12x^55+16x^56+16x^57+7x^58+4x^59

The gray image is a code over GF(2) with n=368, k=15 and d=156.
This code was found by Heurico 1.16 in 8.43 seconds.