The generator matrix

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

generates a code of length 56 over Z16 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+150x^51+241x^52+388x^53+469x^54+552x^55+688x^56+488x^57+434x^58+298x^59+162x^60+96x^61+26x^62+48x^63+7x^64+20x^65+14x^66+8x^67+4x^68+1x^70+1x^84

The gray image is a code over GF(2) with n=448, k=12 and d=204.
This code was found by Heurico 1.16 in 0.434 seconds.