The generator matrix

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

generates a code of length 55 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+12x^54+88x^55+14x^56+4x^58+8x^59+1x^64

The gray image is a code over GF(2) with n=440, k=7 and d=216.
This code was found by Heurico 1.16 in 0.114 seconds.