The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  1  2 12  1  1  2  1  0  1  1  2 12  1  1  0  2  1 12  1  2  1  1  2  2  1  1  0  1  1  1  2  2
 0  2 12  6  0  6 12 10  0  6 12 10  0  6  6  2 12 10 10  2  6  0  6 10  2 12  0 10  2  6 10  2  6  6  2 10 10 12  0  0  6  6 12  2 10  4  6  6  0
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  8  8  8  0  0  8  8  0  8  8  8  0  0  8  0  8  0  0  0  8  0  8  8  8  0  0  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  0  0  8  8  8  0  8  0  8  8  0  0  0  8  0  8  0  8  8  8  0  8  0
 0  0  0  0  8  0  0  0  0  0  8  0  8  0  0  8  8  8  0  0  8  8  8  0  0  8  0  8  0  8  8  0  8  8  0  0  0  0  0  0  8  8  0  8  8  0  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  0  8  0  0  0  0  8  8  0  8  0  8  8  0  0  8  0  8  8  0  8  8  8  0  8  0  0  8
 0  0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  8  8  0  8  0  0  0  8  0  8  8  8  0  8  0  8  0  0  0  0  0  8  8  8  0  0  8  0  0  8  8  8  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  0  8  0  8  8  8  0  8  0  0  8  8  8  8  0  8  0  0  8  0  8  0  0  8  0  8  8  8  8  8  8  8  0  0  8  8
 0  0  0  0  0  0  0  0  8  0  8  0  8  0  8  0  0  8  8  8  8  8  0  0  0  8  0  0  8  0  0  8  8  0  8  8  0  0  8  0  8  8  0  0  8  0  0  0  0
 0  0  0  0  0  0  0  0  0  8  0  8  0  0  8  0  8  8  8  0  8  0  0  8  8  0  0  8  0  8  8  0  8  0  8  0  0  8  0  0  0  8  8  0  8  0  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+60x^38+170x^40+40x^41+354x^42+224x^43+941x^44+928x^45+3198x^46+2336x^47+6516x^48+3184x^49+6578x^50+2336x^51+3255x^52+928x^53+914x^54+224x^55+306x^56+40x^57+134x^58+59x^60+18x^62+15x^64+6x^66+1x^68+2x^70

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 15.2 seconds.