The generator matrix

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

generates a code of length 49 over Z16 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+70x^41+147x^42+308x^43+709x^44+1300x^45+2565x^46+3814x^47+4673x^48+5498x^49+5056x^50+3746x^51+2403x^52+1246x^53+635x^54+286x^55+135x^56+72x^57+40x^58+34x^59+12x^60+6x^61+4x^62+4x^63+3x^64+1x^66

The gray image is a code over GF(2) with n=392, k=15 and d=164.
This code was found by Heurico 1.16 in 9.76 seconds.