The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+129x^42+176x^43+663x^44+684x^45+1519x^46+1628x^47+2367x^48+2236x^49+2356x^50+1628x^51+1395x^52+612x^53+543x^54+148x^55+167x^56+52x^57+54x^58+4x^59+10x^60+6x^62+5x^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 3.67 seconds.