The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  4  1  2  4  2  4  2
 0 12  0  0  0  0  0  0  0 12 12  4  4  4  4  4  0 12  4  8  0  8  0  4  8  4 12  8  8 12 12  0  4  0 12  0  4 12 12 12  4  8  4  8  4  4 12  8
 0  0 12  0  0  0  4 12  4  4 12  8  4  8  8  4  0  4 12 12  4  8  8 12  8  0  0  4  8 12  0  8  0  4 12 12  0  0  0  8  8 12  0  0  0 12  8  0
 0  0  0 12  0  4  4 12  0  8 12 12 12 12  8  0 12  0  4  0  0  4  8 12  4  8  4  4  4  0  4 12  0  4  4  4  0  0  8  0 12 12  4  4  4 12 12  0
 0  0  0  0 12  4  0 12  4 12  8  4 12  8 12  0  4  4  0 12  0  0  8 12  0 12  4  0 12  8  4 12  8  8  4 12  4  8 12  0  0  8  8  0  0 12 12  4
 0  0  0  0  0  8  0  0  8  8  0  8  0  0  8  8  0  0  0  0  8  8  0  8  0  8  0  8  8  0  0  8  8  0  0  0  8  8  8  0  0  0  8  0  8  0  8  0
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  8  8  0  8  0  0  0  0  8  8  8  0  8  0  8  0  0  0  0  8  0  8  0  8  8  8  0  8  0  0  8  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  0  8  0  0  8  8  8  0  8  8  8  0  0  0  0  0  0  8  8  0  8  0  8  0  0  8  0  8  8  8  8  8  0  0  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+167x^38+503x^40+751x^42+64x^43+1181x^44+832x^45+3680x^46+5248x^47+7898x^48+5248x^49+3735x^50+832x^51+1222x^52+64x^53+699x^54+405x^56+177x^58+53x^60+6x^62+1x^66+1x^80

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 18.3 seconds.