The generator matrix

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

generates a code of length 41 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+24x^30+68x^31+133x^32+218x^33+306x^34+458x^35+620x^36+850x^37+2115x^38+3580x^39+4921x^40+6036x^41+5063x^42+3572x^43+2206x^44+900x^45+570x^46+428x^47+269x^48+178x^49+100x^50+82x^51+36x^52+10x^53+11x^54+4x^55+3x^56+3x^58+2x^60+1x^64

The gray image is a code over GF(2) with n=328, k=15 and d=120.
This code was found by Heurico 1.16 in 13.5 seconds.