The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  1  2  2  1  2  1  2  1  2  1
 0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  8  0  8  8  8  0  0  8  8  8  8  8  8  0  8  8  8  0  8  0
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  8  8  8  8  8  8  0  0  0  0  0  8  8  8  8  8  8  8  0  0  0  8  0  8  8  8  0  8  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  8  8  0  8  8  8  0  8  0  0  8  8  0  0  0  8  8  8  0  0  8  8  8  8  8  8
 0  0  0  0  8  0  0  0  0  0  0  8  0  8  8  0  8  8  8  0  8  8  8  0  0  0  0  0  8  0  0  8  8  8  0  8  8  0  8  8  0  0  0  8  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  8  0  0  8  0  0  8  8  0  0  0  8  8  0  8  0  8  0  8  8  8  0  0  0  8  0  8
 0  0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  0  0  8  0  0  8  8  0  8  0  8  0  8  0  8  0  8  8  8  8  0  0  0  8  0  0  8  0  0
 0  0  0  0  0  0  0  8  0  0  8  0  0  8  0  0  8  0  0  8  0  8  8  0  0  8  8  8  0  0  8  8  0  8  8  0  8  0  0  8  0  0  8  8  8
 0  0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  0  0  8  0  0  0  8  8  8  8  0  0  0  8  0  8  8  8  0  8  8  8  8  0  0  0  8  0  0
 0  0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  8  8  8  0  8  0  8  0  8  0  8  8  0  0  8  0  8  8  8  8  0  8  8  0  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+39x^34+91x^36+124x^38+152x^40+269x^42+381x^44+6144x^45+338x^46+253x^48+153x^50+101x^52+80x^54+39x^56+19x^58+3x^60+2x^62+2x^64+1x^72

The gray image is a code over GF(2) with n=360, k=13 and d=136.
This code was found by Heurico 1.16 in 1.31 seconds.