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

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

Homogenous weight enumerator: w(x)=1x^0+68x^38+78x^39+176x^40+254x^41+344x^42+400x^43+536x^44+990x^45+1892x^46+3428x^47+5193x^48+6048x^49+5054x^50+3522x^51+2055x^52+972x^53+525x^54+364x^55+297x^56+218x^57+163x^58+78x^59+61x^60+30x^61+15x^62+2x^63+1x^64+2x^66+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.