The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+53x^30+32x^31+152x^32+180x^33+287x^34+444x^35+566x^36+916x^37+1137x^38+4616x^39+1902x^40+12128x^41+1931x^42+4704x^43+1122x^44+960x^45+551x^46+408x^47+289x^48+140x^49+117x^50+36x^51+55x^52+12x^53+19x^54+8x^56+1x^58+1x^68

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 13.7 seconds.