The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  0  1  1  6  1  1 12  1  1 10  1  1  1  1  6  0  1  1  1  1  1 10 12  1  6  0  1  1  1  1 10  6  1  1 10  1  1  1  0  1  1  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  1  0  5  1  6  3  1 15 12  1  9 10  3  0  1  1  5  6 15  9  5  1  1  9  1  1 12  3 10  0  1  1  6  5  1  0 12  5  1  3  3  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  8  8  8  8  0  0  8  8  0  0  0  8  0  0  8  0  0  8  0  0  8  8  8  0  8  8  0  0  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  8  0  8  0  0  8  0  8  8  8  8  0  8  8  8  0  0  8  0  8  8  8  0  8  0  8  0  0  0  0  8  8  8  8  0  8  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  8  8  0  0  8  0  8  0  8  8  8  8  0  0  8  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  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  8  8  8  0  0  8  8  0  8  0  0  0  0  8  8  0  8  0  8  0  8  8  8  0  8  0  0  8  0  8  8  8  0  0  0  8  0
 0  0  0  0  0  0  8  0  0  8  8  0  0  8  8  0  0  8  8  0  0  0  8  8  0  8  0  0  8  0  8  8  0  0  8  0  0  8  0  0  8  8  8  8  8  8  8  8  8  0  0  0  8  8  0
 0  0  0  0  0  0  0  8  0  8  0  0  0  0  0  0  8  8  0  8  0  8  8  0  8  8  8  0  8  8  0  8  8  8  8  8  8  0  0  8  0  0  8  0  8  0  8  0  0  0  0  0  8  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  8  0  8  0  0  8  8  0  8  0  8  0  8  8  8  0  8  0  8  0  8  8  8  8  8  8  0  0  8  0  8  0  8  0  0  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+22x^44+8x^45+67x^46+72x^47+187x^48+280x^49+683x^50+1248x^51+2725x^52+3296x^53+5545x^54+4528x^55+5558x^56+3296x^57+2721x^58+1248x^59+652x^60+280x^61+153x^62+72x^63+58x^64+8x^65+33x^66+9x^68+11x^70+4x^72+3x^74

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 10.6 seconds.