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

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

Homogenous weight enumerator: w(x)=1x^0+70x^44+132x^45+178x^46+262x^47+419x^48+448x^49+760x^50+1072x^51+2351x^52+3520x^53+4454x^54+5448x^55+4393x^56+3594x^57+2356x^58+1178x^59+779x^60+390x^61+340x^62+184x^63+150x^64+94x^65+99x^66+46x^67+23x^68+14x^69+4x^70+2x^71+5x^72+1x^76+1x^82

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 seconds.