The generator matrix

 1  0  1  1  4  1 10  1  1  1  1  6 10  1  1  1  1  4  1  1 10  1  1  8  4 14  2  0  1  1  1  1  1  1  1  1 10  0 12  1  1  1  2  1  0  1  1  1  4  1  1  1  1  1  1
 0  1  1  6  1  7  1  4 15  2  5  1  1  8  3 14 13  1 10  9  1  0 15  1  1  1  1  1 14  2  2 12  0 14 12 12  1  1  1  3  1  9  1 11  1  7  1  7  1 10  5  5  8  7  2
 0  0  2  0 10  2  6 10  8 10  8  0 10 14  6 14  6  6  0  8  0  0  8  4 12  4  4  0 12 12 14 10  6  2 12 12 14  6 10 10 12  6  2  4 14 12  6 14  8  8 12  4  2 10  4
 0  0  0  8  0  8  8  8  8  0  0  8  8  8  8  0  0  0  0  8  0  8  0  8  0  8  0  8  0  8  8  0  0  8  0  8  0  8  8  0  8  8  0  0  8  8  0  8  8  8  0  8  0  0  0

generates a code of length 55 over Z16 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+236x^51+412x^52+742x^53+428x^54+580x^55+432x^56+632x^57+370x^58+172x^59+6x^60+46x^61+8x^62+20x^63+4x^64+4x^65+1x^72+2x^74

The gray image is a code over GF(2) with n=440, k=12 and d=204.
This code was found by Heurico 1.16 in 0.309 seconds.