The generator matrix

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

generates a code of length 55 over Z16 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+2x^45+73x^46+38x^47+148x^48+106x^49+173x^50+224x^51+516x^52+924x^53+1155x^54+1516x^55+1167x^56+908x^57+513x^58+240x^59+145x^60+98x^61+104x^62+30x^63+53x^64+10x^65+16x^66+10x^68+11x^70+7x^72+1x^74+1x^76+1x^78+1x^82

The gray image is a code over GF(2) with n=440, k=13 and d=180.
This code was found by Heurico 1.16 in 3.5 seconds.