The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  6  1  1  1  0  1  1  1 12  1 10  1  0  1  1  6  1 12  1  1  1 10  1  1  1  6  0  1  1  1  6  0  1  1  6  1
 0  1  3  6  5  1 12  7  1 10  9  1  6  1  3  0  5  1 15 12 10  1  9  1  0  1  3  5  1  6  1 12 15 10  1  0  9 12  1  1  3  6  0  1  2  3  3  1  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  0  8  0  8  0  8  8  0  8  8  8  0  0  0  0  0  8  0  0  8  0  8  8  8  0  8  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  8  0  0  0  0  0  0  0  8  8  0  8  8  8  8  8  0  8  0  0  0  8  8  8  0  8  0  8  8  8  8  0  0  0  8  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  0  0  8  8  8  8  8  0  8  8  0  8  0  0  8  8  0  8  8  8  8  0  8  0  0  0  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  0  8  8  0  0  8  8  8  8  0  0  8  8  0  0  0  8  0  0  8  0  0  0  8  0  8
 0  0  0  0  0  0  8  0  0  0  8  0  8  0  8  8  8  0  0  0  8  8  8  8  0  8  0  0  8  8  8  0  8  8  0  0  0  8  8  8  0  0  0  0  8  0  8  8  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  0  8  0  0  8  0  8  8  8  0  0  0  0  8  0  0  0  8  8  8  8  8  8  0  8  8  0  8  8  8  0  8  0  8
 0  0  0  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  0  8  0  0  8  8  8  8  0  0  8  8  0  0  8  0  8  8  8  8  8  8  0  8  0  8  8  8  0  8
 0  0  0  0  0  0  0  0  0  8  8  0  8  0  8  8  8  0  0  0  8  8  8  8  0  0  8  8  0  0  0  8  0  0  0  8  8  0  0  0  0  0  8  8  8  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+53x^38+18x^39+126x^40+112x^41+183x^42+644x^43+589x^44+3090x^45+4146x^46+8028x^47+10253x^48+11016x^49+10303x^50+8064x^51+4159x^52+3068x^53+558x^54+642x^55+181x^56+120x^57+85x^58+12x^59+35x^60+2x^61+26x^62+14x^64+5x^66+1x^68+1x^70+1x^72

The gray image is a code over GF(2) with n=392, k=16 and d=152.
This code was found by Heurico 1.16 in 34.1 seconds.