The generator matrix

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

generates a code of length 49 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+49x^42+170x^43+287x^44+640x^45+1431x^46+1512x^47+3094x^48+2030x^49+3171x^50+1526x^51+1368x^52+618x^53+250x^54+118x^55+38x^56+34x^57+19x^58+9x^60+6x^61+7x^62+2x^63+3x^64+1x^66

The gray image is a code over GF(2) with n=392, k=14 and d=168.
This code was found by Heurico 1.16 in 2.58 seconds.