The generator matrix

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

generates a code of length 45 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+38x^34+143x^36+286x^38+531x^40+1733x^42+1024x^43+3472x^44+2048x^45+3357x^46+1024x^47+1696x^48+608x^50+247x^52+96x^54+43x^56+21x^58+10x^60+5x^62+1x^64

The gray image is a code over GF(2) with n=360, k=14 and d=136.
This code was found by Heurico 1.16 in 4.66 seconds.