The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  2  2  1  4  2  0  1  1  4  2  1  1  0  1  1  1  1  1  4  1  2  2  1  1  2
 0 12  0 12  0 12  0 12  0 12  8  4  0 12  0  8 12  4 12  0  0 12  4 12 12 12  0 12 12  4  0  8 12 12  0 12  4 12 12  8 12  4 12  8  0  0  4  8  0
 0  0  8  0  0  0  0  0  0  0  8  0  8  0  0  8  0  0  0  8  0  8  8  8  8  0  8  0  8  0  8  0  0  8  8  0  8  0  0  8  8  8  0  8  0  8  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  8  0  8  0  0  0  8  0  8  8  8  8  0  8  0  8  8  0  0  8  0  8  0  8  0  0  8  0  8  0  0  8  8  0  8  8  8  8
 0  0  0  0  8  0  0  0  0  0  0  0  8  0  0  8  8  8  0  0  8  0  8  8  8  8  0  0  8  0  8  0  8  8  8  8  0  0  8  8  0  0  8  0  0  8  8  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  0  8  0  0  0  0  8  8  8  0  0  0  8  8  8  8  8  8  8  8  0  8  8  0  0  0  0  8  8  8  8  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  0  0  0  8  8  8  8  0  0  8  0  0  8  0  0  8  8  0  0  0  8  0  0  8  0  8  0
 0  0  0  0  0  0  0  8  0  0  0  0  0  8  0  0  0  8  8  0  0  0  0  8  8  0  8  8  0  8  0  0  8  8  8  8  0  0  8  8  0  8  8  8  0  0  0  8  0
 0  0  0  0  0  0  0  0  8  0  8  0  8  0  8  8  0  0  0  8  0  8  8  8  0  8  0  8  0  0  0  8  8  8  0  0  0  0  8  8  0  0  8  8  8  0  0  8  8
 0  0  0  0  0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  8  0  0  8  8  0  8  0  8  0  8  0  8  8  0  8  8  8  8  0  8  0  8  0  0  0  8  8  8  0

generates a code of length 49 over Z16 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+71x^38+158x^40+248x^42+545x^44+1703x^46+1024x^47+3424x^48+2048x^49+3452x^50+1024x^51+1708x^52+511x^54+243x^56+120x^58+49x^60+33x^62+13x^64+4x^66+2x^68+2x^70+1x^72

The gray image is a code over GF(2) with n=392, k=14 and d=152.
This code was found by Heurico 1.16 in 11.3 seconds.