The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+36x^30+2x^31+97x^32+60x^33+208x^34+384x^35+755x^36+1674x^37+4799x^38+7284x^39+11523x^40+11896x^41+11520x^42+7312x^43+4803x^44+1668x^45+743x^46+378x^47+185x^48+60x^49+80x^50+41x^52+2x^53+21x^54+1x^56+1x^60+1x^62+1x^64

The gray image is a code over GF(2) with n=328, k=16 and d=120.
This code was found by Heurico 1.16 in 23.8 seconds.