The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+46x^40+186x^41+835x^42+1108x^43+3103x^44+4496x^45+7778x^46+9604x^47+11282x^48+9584x^49+7922x^50+4464x^51+2984x^52+1064x^53+720x^54+164x^55+108x^56+30x^57+19x^58+20x^59+9x^60+6x^62+3x^64

The gray image is a code over GF(2) with n=384, k=16 and d=160.
This code was found by Heurico 1.16 in 25.8 seconds.