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

generates a code of length 49 over Z16 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+69x^38+72x^39+190x^40+228x^41+310x^42+404x^43+603x^44+1252x^45+1912x^46+3604x^47+5080x^48+5224x^49+5141x^50+3640x^51+1939x^52+1288x^53+597x^54+416x^55+302x^56+180x^57+147x^58+52x^59+65x^60+20x^61+14x^62+4x^63+11x^64+1x^68+1x^74+1x^82

The gray image is a code over GF(2) with n=392, k=15 and d=152.
This code was found by Heurico 1.16 in 18.6 seconds.