The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  2 12  1  1  1  1  2  2  2  1  8  4  1  1  1  2  0  2  2  1  1  1  4  1  8  1 12  2  1  2  1  1  1  4  2  1
 0  2  0 14  4  6 12  2  0  6 14 12  8  2 10  4  6  2  6 10  2  0  8 14  2 14  6  2  6  2  2  4 14 12 14  2  8 10 10  0  4  4 10  2 14  2  4  6  6  8 14 10  4  0  0
 0  0 12  4  4  0  0  4  0  0  4  8  4 12  8  4  8  0  8  8  8  0  4 12  4 12  0  4  8 12  4 12  0  4 12  0  4  0 12  8  4 12  8  4  4  0 12  4  0  4  8  0  4  0  0
 0  0  0  8  0  0  0  0  0  0  8  0  0  0  0  0  8  8  0  8  8  0  8  8  8  0  8  0  8  8  8  8  8  0  8  0  8  8  0  8  8  8  8  0  0  0  8  8  8  8  8  0  8  0  0
 0  0  0  0  8  0  0  0  0  8  8  8  8  0  0  8  0  8  0  0  8  0  8  8  0  0  8  8  0  8  0  0  0  8  0  8  8  0  0  8  8  8  8  0  8  8  0  0  0  0  8  8  0  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  0  8  0  8  0  0  0  8  8  8  8  8  8  0  8  0  8  8  0  8  8  8  0  0  8  0  8  0  8  0  0  8  8  0  8  0  8  0
 0  0  0  0  0  0  8  0  0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  0  0  8  8  8  8  8  8  0  0  0  8  0  0  0  8  8  0  0  0  8  8  8  0
 0  0  0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  8  8  8  0  8  0  8  8  8  0  8  0  8  8  8  0  0  0  8  0  8  0  8  8  8  0  0  0  0  0  0  0  8  0  0  8  0  0
 0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  0  0  0  8  8  0  8  0  0  8  8  0  0  0  8  8  0  8  0  8  0  8  8  0  8  8  0  0  8  0  0  8  0  0  0  8  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+42x^44+60x^45+122x^46+236x^47+387x^48+554x^49+978x^50+1442x^51+2306x^52+3590x^53+4262x^54+4720x^55+4449x^56+3396x^57+2460x^58+1564x^59+888x^60+536x^61+318x^62+212x^63+84x^64+50x^65+34x^66+18x^67+26x^68+6x^69+18x^70+7x^72+2x^76

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 17.4 seconds.