The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+179x^42+124x^43+749x^44+448x^45+1570x^46+1408x^47+2689x^48+2188x^49+2664x^50+1420x^51+1469x^52+424x^53+642x^54+120x^55+196x^56+12x^57+61x^58+13x^60+4x^62+2x^64+1x^68

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 3.73 seconds.