The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+134x^41+506x^42+1386x^43+3002x^44+4994x^45+7488x^46+9860x^47+10777x^48+10002x^49+7696x^50+4916x^51+2691x^52+1234x^53+512x^54+216x^55+65x^56+16x^57+22x^58+2x^59+7x^60+4x^61+4x^63+1x^64

The gray image is a code over GF(2) with n=384, k=16 and d=164.
This code was found by Heurico 1.16 in 26.8 seconds.