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

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

Homogenous weight enumerator: w(x)=1x^0+41x^38+78x^39+147x^40+252x^41+335x^42+354x^43+589x^44+1076x^45+1895x^46+3388x^47+5184x^48+6076x^49+5224x^50+3388x^51+1933x^52+1108x^53+521x^54+390x^55+265x^56+168x^57+159x^58+82x^59+69x^60+24x^61+15x^62+3x^64+1x^66+1x^68+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 18.3 seconds.