The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  1  4  2  1  4  4  2  1  0  1  8  4  1  0  4  4  0  2  2  4  1
 0 12  0  4  0  0  4 12  0  0 12 12  0  8 12 12  8  0  4 12 12 12  4 12  0  4  8  8  8 12  4  0  4  4  4  4 12  8  0  0  4 12  4  0  8
 0  0 12  4  0 12  4  0  0 12 12  8  8 12  4  0  4  8  4 12  0  0  4  0  8  4  4 12  4  0  4  0  0 12 12 12  0  4 12 12  0  8 12 12  4
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  0  0  8  8  8  8  0  0  8  0  0  8  8  0  8  0  8  8  0  8  0  8  8
 0  0  0  0  8  0  0  0  0  0  0  8  0  0  8  8  8  8  8  0  8  0  0  0  8  0  8  0  0  0  0  8  0  8  0  8  0  8  8  8  8  0  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  8  0  8  8  8  0  0  0  8  8  8  8  0  8  0  0  0  8  0  0  0  8  8  0  8  8  0  0  8  8
 0  0  0  0  0  0  8  0  0  0  8  0  0  0  0  8  0  8  8  8  0  8  8  0  8  0  8  8  8  0  8  8  8  8  8  8  0  8  0  8  0  0  0  0  8
 0  0  0  0  0  0  0  8  0  0  8  0  8  8  0  8  0  0  0  8  8  0  0  8  0  8  0  0  0  0  8  8  8  0  8  0  0  8  0  8  0  8  8  0  0
 0  0  0  0  0  0  0  0  8  0  0  0  8  0  0  8  0  8  0  0  0  0  8  0  8  8  0  8  0  0  8  8  8  8  0  0  8  0  8  8  8  8  0  0  8
 0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  0  8  0  0  0  8  8  8  0  8  0  8  8  0  8  0  8  8  0  8  8  8  0  8  8  8  0  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+57x^34+60x^35+201x^36+190x^37+427x^38+462x^39+940x^40+2126x^41+1843x^42+4186x^43+2658x^44+6132x^45+2669x^46+4900x^47+1888x^48+1604x^49+991x^50+584x^51+381x^52+174x^53+133x^54+46x^55+66x^56+14x^57+21x^58+2x^59+8x^60+3x^62+1x^80

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 19.3 seconds.