The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  1  1  2  1 12  2  1  1  0  1  2  1  1 12  1  2  1  1  1  1  0  2  1  2  1  0  1  1  1  1
 0  2 12  6  0  6 12 10  0  6 12 10  6  2  0  6 12 10 10  2  6  6  0  2 12 10  6  0  2 10  6 10 12  6 12  2 10 14  6 10  2  0  6  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  8  8  8  0  8  8  8  8  8  0  0  8  0  0  0  8  0  8  0  8  0  8  8  0  0  0  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  8  8  0  8  8  0  0  0  0  8  0  8  0  8  8  8  8  8  8  8  0  8  0  8  0  8  0
 0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  0  8  8  0  8  0  8  0  8  0  0  8  0  8  8  8  8  8  0  8  8  0  8  8  0  8  0  0  0  8
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  8  0  8  8  0  8  0  8  0  0  8  0  8
 0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  0  8  0  8  8  0  0  8  0  8  0  8  0  0  8  0  8  0  0  0  8  0  8  0  8  8  0  8  8  0
 0  0  0  0  0  0  0  8  0  0  0  8  8  0  0  0  8  0  8  8  8  8  0  0  0  0  0  0  8  8  8  8  0  8  8  0  0  8  8  0  0  0  0  8  0
 0  0  0  0  0  0  0  0  8  0  8  0  8  0  8  0  0  0  0  8  8  8  0  8  8  0  8  8  8  0  0  0  8  0  0  8  0  8  0  0  8  8  8  8  0
 0  0  0  0  0  0  0  0  0  8  0  8  8  0  0  0  8  8  0  8  0  8  8  0  8  8  8  0  8  0  0  0  8  0  8  8  8  8  8  8  8  8  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+47x^34+12x^35+86x^36+64x^37+267x^38+188x^39+871x^40+960x^41+2304x^42+3896x^43+4625x^44+6144x^45+4642x^46+3896x^47+2304x^48+960x^49+839x^50+188x^51+256x^52+64x^53+63x^54+12x^55+39x^56+26x^58+9x^60+4x^62+1x^64

The gray image is a code over GF(2) with n=360, k=15 and d=136.
This code was found by Heurico 1.16 in 12.6 seconds.