The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  0  1  1  6  1  1 12  1  1 10  1  1  0  1  1  1  1 12  1  1  1  1  1  6  1  1  1  1 12  1  6  6  1  1  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  1  0  5  1  6  3  1 15  9  1 12 10  1  0  6  3  5  1  9  5 15  3 15  1 10 12  6 15  1  6  1  1  6  5  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  8  8  8  8  0  0  8  0  8  8  0  0  0  8  8  8  0  0  0  0  8  0  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  8  0  8  0  0  8  8  8  8  0  8  8  8  8  0  0  8  8  0  8  8  8  0  0  0  0  8  0  8  0  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  8  8  0  8  0  0  8  0  8  8  8  0  8  8  8  0  0  0  0  8  0  8  8  8  0  0  8  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  0  8  8  8  0  8  8  0  0  8  0  8  0  0  0  8  8  0  8  8  8  8  8  0  0  0  8  0  8  0  0  0
 0  0  0  0  0  0  8  0  0  8  8  0  0  8  8  0  0  8  8  0  8  0  0  0  8  8  8  8  0  0  0  8  0  8  8  0  0  8  0  0  0  8  8  8  8  8  8  0
 0  0  0  0  0  0  0  8  0  8  0  0  0  0  0  0  8  8  0  8  8  0  8  8  8  0  0  8  8  8  0  8  0  0  8  8  0  8  8  8  0  0  0  8  8  8  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  8  0  8  0  8  0  8  8  8  8  8  8  8  8  0  0  8  0  8  8  8  0  8  0  8  0  8  0  8  0  0

generates a code of length 48 over Z16 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+23x^38+16x^39+92x^40+116x^41+193x^42+748x^43+829x^44+3108x^45+2594x^46+6764x^47+3836x^48+6764x^49+2593x^50+3108x^51+807x^52+748x^53+184x^54+116x^55+52x^56+16x^57+27x^58+11x^60+14x^62+3x^64+3x^66+1x^68+1x^70

The gray image is a code over GF(2) with n=384, k=15 and d=152.
This code was found by Heurico 1.16 in 8.72 seconds.