The generator matrix

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

generates a code of length 42 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+65x^30+26x^31+136x^32+74x^33+175x^34+198x^35+394x^36+402x^37+1200x^38+1608x^39+4592x^40+3828x^41+7354x^42+3836x^43+4584x^44+1620x^45+1214x^46+410x^47+426x^48+194x^49+176x^50+62x^51+74x^52+26x^53+48x^54+4x^55+28x^56+6x^58+4x^60+1x^62+1x^64+1x^66

The gray image is a code over GF(2) with n=336, k=15 and d=120.
This code was found by Heurico 1.16 in 17.4 seconds.