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  2  1  2  2  4  2  1  1  2  4  1  2  1  2  0  1  8  8  4  2  8  2  1  1  1
 0 12  0  0  0  4 12  4  0  8  4 12  0  8 12  0  4  4  8  4 12 12  8  8 12 12  0 12  4  8  0  4  8 12 12  8  0  4 12  4  4 12  0  4  0  8  4  4 12  4  4  8  4  8  0
 0  0 12  0  4  4 12  0  0  0  4  8  4  4  0  8  4  4 12  8 12  0  8  8  4  0 12  0 12  8  4  4 12  4 12  4  8 12  4 12 12  0 12  0  8  0  4  0  8  0 12 12  8  4  8
 0  0  0 12  4  0 12  4  0  4 12  8 12  0  4  8  8  8  4  0  4  4 12  4  4  4 12  8  0  8 12  8 12 12 12  8 12  8 12  8  4  0  4  4  4  0  8 12  0  8  0  0  8  0  4
 0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  0  8  8  8  0  8  8  0  0  0  8  0  8  0  8  8  0  8  8  8  8  8  0  0  0  0  0  8  0  0  8  0  8  8  0  0  0  8  0  0
 0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  8  0  8  8  0  8  8  0  8  0  0  0  0  8  0  0  0  8  8  0  0  8  8  0  8  0  8  8  8  0  0  8  0  8  0  8  0  0  8  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  8  8  8  8  0  0  0  0  8  8  8  8  8  0  0  8  8  8  0  0  8  8  0  0  0  0  8  0  0  8  8  8  0  8  0  0  8
 0  0  0  0  0  0  0  8  8  8  0  8  0  0  0  0  0  8  0  8  8  0  8  0  8  8  0  0  0  8  0  8  8  8  0  0  8  8  8  0  0  8  8  0  8  8  0  0  8  0  8  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+44x^45+101x^46+118x^47+225x^48+292x^49+384x^50+740x^51+1020x^52+1734x^53+2422x^54+2354x^55+2384x^56+1738x^57+973x^58+742x^59+340x^60+242x^61+182x^62+128x^63+100x^64+42x^65+26x^66+14x^67+24x^68+4x^69+6x^70+2x^72+1x^74+1x^78

The gray image is a code over GF(2) with n=440, k=14 and d=180.
This code was found by Heurico 1.16 in 6.09 seconds.