The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+28x^41+156x^42+362x^43+868x^44+1158x^45+2063x^46+2056x^47+3053x^48+2120x^49+2101x^50+1064x^51+813x^52+274x^53+112x^54+72x^55+28x^56+16x^57+13x^58+14x^59+5x^60+4x^61+3x^62

The gray image is a code over GF(2) with n=384, k=14 and d=164.
This code was found by Heurico 1.16 in 2.56 seconds.