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

generates a code of length 55 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+153x^44+382x^46+16x^47+706x^48+144x^49+1252x^50+864x^51+2747x^52+2928x^53+4917x^54+4384x^55+5044x^56+2928x^57+2931x^58+864x^59+1232x^60+144x^61+588x^62+16x^63+306x^64+150x^66+43x^68+17x^70+6x^72+3x^74+1x^76+1x^80

The gray image is a code over GF(2) with n=440, k=15 and d=176.
This code was found by Heurico 1.16 in 22.2 seconds.