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

generates a code of length 50 over Z16 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+50x^38+30x^39+127x^40+154x^41+269x^42+276x^43+640x^44+882x^45+1607x^46+2214x^47+3304x^48+4620x^49+4348x^50+4608x^51+3418x^52+2252x^53+1608x^54+946x^55+559x^56+250x^57+253x^58+108x^59+113x^60+34x^61+47x^62+10x^63+25x^64+10x^66+4x^68+1x^76

The gray image is a code over GF(2) with n=400, k=15 and d=152.
This code was found by Heurico 1.16 in 18.9 seconds.